-
Previous Article
Center Lyapunov exponents in partially hyperbolic dynamics
- JMD Home
- This Issue
-
Next Article
Lectures on dynamics, fractal geometry, and metric number theory
Rigidity of Julia sets for Hénon type maps
1. | Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore 119076, Singapore |
2. | Université Paris-Sud, Mathématique - Bâtiment 425, 91405 Orsay, France |
References:
[1] |
L. V. Ahlfors, Zur Theorie der Überlagerungsflächen, Acta Math., 65 (1935), 157-194.
doi: 10.1007/BF02420945. |
[2] |
L. V. Ahlfors and L. Sario, Riemann Surfaces, Princeton Mathematical Series, No. 26, Princeton University Press, Princeton, N.J. 1960. |
[3] |
E. Bedford and K. Kim, Dynamics of rational surface automorphisms: Rotation domains, Amer. J. Math., 134 (2012), 379-405.
doi: 10.1353/ajm.2012.0015. |
[4] |
E. Bedford, M. Lyubich and J. Smillie, Distribution of periodic points of polynomial diffeomorphisms of $C^2$, Invent. Math., 114 (1993), 277-288.
doi: 10.1007/BF01232671. |
[5] |
E. Bedford, M. Lyubich and J. Smillie, Polynomial diffeomorphisms of $C^2$. IV. The measure of maximal entropy and laminar currents, Invent. Math., 112 (1993), 77-125.
doi: 10.1007/BF01232426. |
[6] |
E. Bedford and J. Smillie, Polynomial diffeomorphisms of $C^2$: Currents, equilibrium measure and hyperbolicity, Invent. Math., 103 (1991), 69-99.
doi: 10.1007/BF01239509. |
[7] |
E. Bedford and J. Smillie, Polynomial diffeomorphisms of $C^2$. III. Ergodicity, exponents and entropy of the equilibrium measure, Math. Ann., 294 (1992), 395-420.
doi: 10.1007/BF01934331. |
[8] |
J.-B. Bost, H. Gillet and C. Soulé, Heights of projective varieties and positive Green forms, J. Amer. Math. Soc., 7 (1994), 903-1027.
doi: 10.1090/S0894-0347-1994-1260106-X. |
[9] |
D. Burns and N. Sibony, Limit currents and value distribution of holomorphic maps, Ann. Inst. Fourier (Grenoble), 62 (2012), 145-176.
doi: 10.5802/aif.2703. |
[10] |
S. Cantat, Dynamique des automorphismes des surfaces K3, Acta Math., 187 (2001), 1-57.
doi: 10.1007/BF02392831. |
[11] |
S. Cantat, Croissance des variétés instables, Ergodic Theory Dynam. Systems, 23 (2003), 1025-1042.
doi: 10.1017/S0143385702001591. |
[12] |
D. Coman and V. Guedj, Invariant currents and dynamical Lelong numbers, J. Geom. Anal., 14 (2004), 199-213.
doi: 10.1007/BF02922068. |
[13] |
J.-P. Demailly, Regularization of closed positive currents and intersection theory, J. Algebraic Geom., 1 (1992), 361-409. |
[14] |
J.-P. Demailly, Complex Analytic and Differential Geometry., Available from: , ().
|
[15] |
J.-P. Demailly and M. Paun, Numerical characterization of the Kähler cone of a compact Kähler manifold, Ann. of Math. (2), 159 (2004), 1247-1274.
doi: 10.4007/annals.2004.159.1247. |
[16] |
H. De Thélin, Sur la laminarité de certains courants, Ann. Sci. École Norm. Sup. (4), 37 (2004), 304-311.
doi: 10.1016/j.ansens.2003.06.002. |
[17] |
H. De Thélin, Sur les automorphismes réguliers de $\mathbbC^k$, Publ. Mat., 54 (2010), 243-262.
doi: 10.5565/PUBLMAT_54110_14. |
[18] |
H. De Thélin and T.-C. Dinh, Dynamics of automorphisms on compact Kähler manifolds, Adv. Math., 229 (2012), 2640-2655.
doi: 10.1016/j.aim.2012.01.014. |
[19] |
T.-C. Dinh, Decay of correlations for Hénon maps, Acta Math., 195 (2005), 253-264.
doi: 10.1007/BF02588081. |
[20] |
T.-C. Dinh, Suites d'applications méromorphes multivaluées et courants laminaires, J. Geom. Anal., 15 (2005), 207-227.
doi: 10.1007/BF02922193. |
[21] |
T.-C. Dinh and V.-A. Nguyên, The mixed Hodge-Riemann bilinear relations for compact Kähler manifolds, Geom. Funct. Anal., 16 (2006), 838-849.
doi: 10.1007/s00039-006-0572-9. |
[22] |
T.-C. Dinh, V.-A. Nguyên and N. Sibony, Heat equation and ergodic theorems for Riemann surface laminations, Math. Ann., 354 (2012), 331-376.
doi: 10.1007/s00208-011-0730-8. |
[23] |
T.-C. Dinh, V.-A. Nguyên and N. Sibony, Dynamics of horizontal-like maps in higher dimension, Adv. Math., 219 (2008), 1689-1721.
doi: 10.1016/j.aim.2008.07.006. |
[24] |
T.-C. Dinh and N. Sibony, Groupes commutatifs d'automorphismes d'une variété kählérienne compacte, Duke Math. J., 123 (2004), 311-328.
doi: 10.1215/S0012-7094-04-12323-1. |
[25] |
T.-C. Dinh and N. Sibony, Regularization of currents and entropy, Ann. Sci. École Norm. Sup. (4), 37 (2004), 959-971.
doi: 10.1016/j.ansens.2004.09.002. |
[26] |
T.-C. Dinh and N. Sibony, Green currents for holomorphic automorphisms of compact Kähler manifolds, J. Am. Math. Soc., 18 (2005), 291-312.
doi: 10.1090/S0894-0347-04-00474-6. |
[27] |
T.-C. Dinh and N. Sibony, Dynamics of regular birational maps in $P^k$, J. Funct. Anal., 222 (2005), 202-216.
doi: 10.1016/j.jfa.2004.07.018. |
[28] |
T.-C. Dinh and N. Sibony, Geometry of currents, intersection theory and dynamics of horizontal-like maps, Ann. Inst. Fourier (Grenoble), 56 (2006), 423-457.
doi: 10.5802/aif.2188. |
[29] |
T.-C. Dinh and N. Sibony, Super-potentials of positive closed currents, intersection theory and dynamics, Acta Math., 203 (2009), 1-82.
doi: 10.1007/s11511-009-0038-7. |
[30] |
T.-C. Dinh and N. Sibony, Super-potentials for currents on compact Kähler manifolds and dynamics of automorphisms, J. Algebraic Geom., 19 (2010), 473-529.
doi: 10.1090/S1056-3911-10-00549-7. |
[31] |
T.-C. Dinh and N. Sibony, Dynamics in several complex variables: Endomorphisms of projective spaces and polynomial-like mappings, in Holomorphic Dynamical Systems, Lecture Notes in Math., 1998, Springer, Berlin, 2010, 165-294.
doi: 10.1007/978-3-642-13171-4_4. |
[32] |
T.-C. Dinh and N. Sibony, Exponential mixing for automorphisms on compact Kähler manifolds, in Dynamical Numbers-Interplay Between Dynamical Systems and Number Theory, Contemp. Math., 532, Amer. Math. Soc., Providence, RI, 2010, 107-114.
doi: 10.1090/conm/532/10486. |
[33] |
T.-C. Dinh and N. Sibony, Equidistribution of saddle periodic points for Hénon-type automorphisms of $\mathbbC^k$,, , ().
|
[34] |
R. Dujardin, Hénon-like mappings in $\mathbbC^2$, Amer. J. Math., 126 (2004), 439-472. |
[35] |
J. E. Fornæss and N. Sibony, Complex Hénon mappings in $C^2$ and Fatou-Bieberbach domains, Duke Math. J., 65 (1992), 345-380.
doi: 10.1215/S0012-7094-92-06515-X. |
[36] |
J. E. Fornæss and N. Sibony, Complex dynamics in higher dimensions. Notes partially written by Estela A. Gavosto, in Complex Potential Theory (Montreal, PQ, 1993), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 439, Kluwer Acad. Publ., Dordrecht, 1994, 131-186. |
[37] |
J. E. Fornæss and N. Sibony, Harmonic currents of finite energy and laminations, Geom. Funct. Anal., 15 (2005), 962-1003.
doi: 10.1007/s00039-005-0531-x. |
[38] |
J. E. Fornæss and N. Sibony, Unique ergodicity of harmonic currents on singular foliations of $P^2$, Geom. Funct. Anal., 19 (2010), 1334-1377.
doi: 10.1007/s00039-009-0043-1. |
[39] |
S. Friedland and J. Milnor, Dynamical properties of plane polynomial automorphisms, Ergodic Theory Dynam. Systems, 9 (1989), 67-99.
doi: 10.1017/S014338570000482X. |
[40] |
M. Gromov, Convex sets and Kähler manifolds, in Advances in Differential Geometry and Topology, World Sci. Publ., Teaneck, NJ, 1990, 1-38. |
[41] |
M. Gromov, On the entropy of holomorphic maps, Enseign. Math. (2), 49 (2003), 217-235. |
[42] |
R. C. Gunning, Introduction to Holomorphic Functions of Several Variables. Vol. I, II. Function Theory, The Wadsworth & Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1990. |
[43] |
L. Hörmander, The Analysis of Linear Partial Differential Operators. II. Differential Operators with Constant Coefficients, Reprint of the 1983 original, Classics in Mathematics, Springer-Verlag, Berlin, 2005. |
[44] |
H. W. E. Jung, Über ganze birationale Transformationen der Ebene, J. Reine Angew. Math., 184 (1942), 161-174. |
[45] |
A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, With a supplementary chapter by Katok and L. Mendoza, Encyclopedia of Mathematics and its Applications, 54, Cambridge University Press, Cambridge, 1995.
doi: 10.1017/CBO9780511809187. |
[46] |
A. G. Khovanskii, The geometry of convex polyhedra and algebraic geometry, Uspehi Mat. Nauk., 34 (1979), 160-161. |
[47] |
S. Kobayashi, Hyperbolic Complex Spaces, Grundlehren der Mathematischen Wissenschaften, 318, Springer-Verlag, Berlin, 1998.
doi: 10.1007/978-3-662-03582-5. |
[48] |
P. Lelong, Fonctions Plurisousharmoniques Et Formes Différentielles Positives, Gordon & Breach, Paris-London-New York (Distributed by Dunod éditeur, Paris), 1968. |
[49] |
C. T. McMullen, Dynamics on blowups of the projective plane, Publ. Math. Inst. Hautes Études Sci., 105 (2007), 49-89.
doi: 10.1007/s10240-007-0004-x. |
[50] |
M. McQuillan, Diophantine approximations and foliations, Inst. Hautes Études Sci. Publ. Math., 87 (1998), 121-174. |
[51] |
A. Moncet, Géométrie et dynamique sur les surfaces algébriques réelles, Ph.D thesis, arXiv:1207.0390, 2012. |
[52] |
R. Nevanlinna, Analytic Functions, Translated from the second German edition by P. Emig, {Die Grundlehren der mathematischen Wissenschaften}, Band 162 Springer-Verlag, New York-Berlin, 1970. |
[53] |
K. Oguiso, A remark on dynamical degrees of automorphisms of hyperkähler manifolds, Manuscripta Math., 130 (2009), 101-111.
doi: 10.1007/s00229-009-0271-6. |
[54] |
I. P. Shestakov and U. U. Umirbaev, The tame and the wild automorphisms of polynomial rings in three variables, J. Amer. Math. Soc., 17 (2004), 197-227.
doi: 10.1090/S0894-0347-03-00440-5. |
[55] |
N. Sibony, Dynamique des applications rationnelles de $\mathbbP^k$, in Dynamique et Géométrie Complexes (Lyon, 1997), Panoramas et Synthèses, 8, Soc. Math. France, Paris, 1999, ix-x, xi-xii, 97-185. |
[56] |
T. Uehara, Rational surface automorphisms with positive entropy, arXiv:1009.2143, 2010. |
[57] |
C. Voisin, Théorie de Hodge et Géométrie Algébrique Complexe, Cours Spécialisés, 10, Société Mathématique de France, Paris, 2002.
doi: 10.1017/CBO9780511615344. |
[58] |
J. Taflin, Equidistribution speed towards the Green current for endomorphisms of $ \mathbbP^k$, Adv. Math., 227 (2011), 2059-2081.
doi: 10.1016/j.aim.2011.04.010. |
[59] |
B. Teissier, Du théorème de l'index de Hodge aux inégalités isopérimétriques, C. R. Acad. Sci. Paris Sér. A-B, 288 (1979), A287-A289. |
[60] |
V. A. Timorin, Mixed Hodge-Riemann bilinear relations in a linear context, Funktsional. Anal. i Prilozhen., 32 (1998), 63-68, 96; translation in Funct. Anal. Appl., 32 (1998), 268-272.
doi: 10.1007/BF02463209. |
[61] |
S.-T. Yau, On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation. I, Comm. Pure Appl. Math., 31 (1978), 339-411.
doi: 10.1002/cpa.3160310304. |
[62] |
Y. Yomdin, Volume growth and entropy, Israel J. Math., 57 (1987), 285-300.
doi: 10.1007/BF02766215. |
show all references
References:
[1] |
L. V. Ahlfors, Zur Theorie der Überlagerungsflächen, Acta Math., 65 (1935), 157-194.
doi: 10.1007/BF02420945. |
[2] |
L. V. Ahlfors and L. Sario, Riemann Surfaces, Princeton Mathematical Series, No. 26, Princeton University Press, Princeton, N.J. 1960. |
[3] |
E. Bedford and K. Kim, Dynamics of rational surface automorphisms: Rotation domains, Amer. J. Math., 134 (2012), 379-405.
doi: 10.1353/ajm.2012.0015. |
[4] |
E. Bedford, M. Lyubich and J. Smillie, Distribution of periodic points of polynomial diffeomorphisms of $C^2$, Invent. Math., 114 (1993), 277-288.
doi: 10.1007/BF01232671. |
[5] |
E. Bedford, M. Lyubich and J. Smillie, Polynomial diffeomorphisms of $C^2$. IV. The measure of maximal entropy and laminar currents, Invent. Math., 112 (1993), 77-125.
doi: 10.1007/BF01232426. |
[6] |
E. Bedford and J. Smillie, Polynomial diffeomorphisms of $C^2$: Currents, equilibrium measure and hyperbolicity, Invent. Math., 103 (1991), 69-99.
doi: 10.1007/BF01239509. |
[7] |
E. Bedford and J. Smillie, Polynomial diffeomorphisms of $C^2$. III. Ergodicity, exponents and entropy of the equilibrium measure, Math. Ann., 294 (1992), 395-420.
doi: 10.1007/BF01934331. |
[8] |
J.-B. Bost, H. Gillet and C. Soulé, Heights of projective varieties and positive Green forms, J. Amer. Math. Soc., 7 (1994), 903-1027.
doi: 10.1090/S0894-0347-1994-1260106-X. |
[9] |
D. Burns and N. Sibony, Limit currents and value distribution of holomorphic maps, Ann. Inst. Fourier (Grenoble), 62 (2012), 145-176.
doi: 10.5802/aif.2703. |
[10] |
S. Cantat, Dynamique des automorphismes des surfaces K3, Acta Math., 187 (2001), 1-57.
doi: 10.1007/BF02392831. |
[11] |
S. Cantat, Croissance des variétés instables, Ergodic Theory Dynam. Systems, 23 (2003), 1025-1042.
doi: 10.1017/S0143385702001591. |
[12] |
D. Coman and V. Guedj, Invariant currents and dynamical Lelong numbers, J. Geom. Anal., 14 (2004), 199-213.
doi: 10.1007/BF02922068. |
[13] |
J.-P. Demailly, Regularization of closed positive currents and intersection theory, J. Algebraic Geom., 1 (1992), 361-409. |
[14] |
J.-P. Demailly, Complex Analytic and Differential Geometry., Available from: , ().
|
[15] |
J.-P. Demailly and M. Paun, Numerical characterization of the Kähler cone of a compact Kähler manifold, Ann. of Math. (2), 159 (2004), 1247-1274.
doi: 10.4007/annals.2004.159.1247. |
[16] |
H. De Thélin, Sur la laminarité de certains courants, Ann. Sci. École Norm. Sup. (4), 37 (2004), 304-311.
doi: 10.1016/j.ansens.2003.06.002. |
[17] |
H. De Thélin, Sur les automorphismes réguliers de $\mathbbC^k$, Publ. Mat., 54 (2010), 243-262.
doi: 10.5565/PUBLMAT_54110_14. |
[18] |
H. De Thélin and T.-C. Dinh, Dynamics of automorphisms on compact Kähler manifolds, Adv. Math., 229 (2012), 2640-2655.
doi: 10.1016/j.aim.2012.01.014. |
[19] |
T.-C. Dinh, Decay of correlations for Hénon maps, Acta Math., 195 (2005), 253-264.
doi: 10.1007/BF02588081. |
[20] |
T.-C. Dinh, Suites d'applications méromorphes multivaluées et courants laminaires, J. Geom. Anal., 15 (2005), 207-227.
doi: 10.1007/BF02922193. |
[21] |
T.-C. Dinh and V.-A. Nguyên, The mixed Hodge-Riemann bilinear relations for compact Kähler manifolds, Geom. Funct. Anal., 16 (2006), 838-849.
doi: 10.1007/s00039-006-0572-9. |
[22] |
T.-C. Dinh, V.-A. Nguyên and N. Sibony, Heat equation and ergodic theorems for Riemann surface laminations, Math. Ann., 354 (2012), 331-376.
doi: 10.1007/s00208-011-0730-8. |
[23] |
T.-C. Dinh, V.-A. Nguyên and N. Sibony, Dynamics of horizontal-like maps in higher dimension, Adv. Math., 219 (2008), 1689-1721.
doi: 10.1016/j.aim.2008.07.006. |
[24] |
T.-C. Dinh and N. Sibony, Groupes commutatifs d'automorphismes d'une variété kählérienne compacte, Duke Math. J., 123 (2004), 311-328.
doi: 10.1215/S0012-7094-04-12323-1. |
[25] |
T.-C. Dinh and N. Sibony, Regularization of currents and entropy, Ann. Sci. École Norm. Sup. (4), 37 (2004), 959-971.
doi: 10.1016/j.ansens.2004.09.002. |
[26] |
T.-C. Dinh and N. Sibony, Green currents for holomorphic automorphisms of compact Kähler manifolds, J. Am. Math. Soc., 18 (2005), 291-312.
doi: 10.1090/S0894-0347-04-00474-6. |
[27] |
T.-C. Dinh and N. Sibony, Dynamics of regular birational maps in $P^k$, J. Funct. Anal., 222 (2005), 202-216.
doi: 10.1016/j.jfa.2004.07.018. |
[28] |
T.-C. Dinh and N. Sibony, Geometry of currents, intersection theory and dynamics of horizontal-like maps, Ann. Inst. Fourier (Grenoble), 56 (2006), 423-457.
doi: 10.5802/aif.2188. |
[29] |
T.-C. Dinh and N. Sibony, Super-potentials of positive closed currents, intersection theory and dynamics, Acta Math., 203 (2009), 1-82.
doi: 10.1007/s11511-009-0038-7. |
[30] |
T.-C. Dinh and N. Sibony, Super-potentials for currents on compact Kähler manifolds and dynamics of automorphisms, J. Algebraic Geom., 19 (2010), 473-529.
doi: 10.1090/S1056-3911-10-00549-7. |
[31] |
T.-C. Dinh and N. Sibony, Dynamics in several complex variables: Endomorphisms of projective spaces and polynomial-like mappings, in Holomorphic Dynamical Systems, Lecture Notes in Math., 1998, Springer, Berlin, 2010, 165-294.
doi: 10.1007/978-3-642-13171-4_4. |
[32] |
T.-C. Dinh and N. Sibony, Exponential mixing for automorphisms on compact Kähler manifolds, in Dynamical Numbers-Interplay Between Dynamical Systems and Number Theory, Contemp. Math., 532, Amer. Math. Soc., Providence, RI, 2010, 107-114.
doi: 10.1090/conm/532/10486. |
[33] |
T.-C. Dinh and N. Sibony, Equidistribution of saddle periodic points for Hénon-type automorphisms of $\mathbbC^k$,, , ().
|
[34] |
R. Dujardin, Hénon-like mappings in $\mathbbC^2$, Amer. J. Math., 126 (2004), 439-472. |
[35] |
J. E. Fornæss and N. Sibony, Complex Hénon mappings in $C^2$ and Fatou-Bieberbach domains, Duke Math. J., 65 (1992), 345-380.
doi: 10.1215/S0012-7094-92-06515-X. |
[36] |
J. E. Fornæss and N. Sibony, Complex dynamics in higher dimensions. Notes partially written by Estela A. Gavosto, in Complex Potential Theory (Montreal, PQ, 1993), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 439, Kluwer Acad. Publ., Dordrecht, 1994, 131-186. |
[37] |
J. E. Fornæss and N. Sibony, Harmonic currents of finite energy and laminations, Geom. Funct. Anal., 15 (2005), 962-1003.
doi: 10.1007/s00039-005-0531-x. |
[38] |
J. E. Fornæss and N. Sibony, Unique ergodicity of harmonic currents on singular foliations of $P^2$, Geom. Funct. Anal., 19 (2010), 1334-1377.
doi: 10.1007/s00039-009-0043-1. |
[39] |
S. Friedland and J. Milnor, Dynamical properties of plane polynomial automorphisms, Ergodic Theory Dynam. Systems, 9 (1989), 67-99.
doi: 10.1017/S014338570000482X. |
[40] |
M. Gromov, Convex sets and Kähler manifolds, in Advances in Differential Geometry and Topology, World Sci. Publ., Teaneck, NJ, 1990, 1-38. |
[41] |
M. Gromov, On the entropy of holomorphic maps, Enseign. Math. (2), 49 (2003), 217-235. |
[42] |
R. C. Gunning, Introduction to Holomorphic Functions of Several Variables. Vol. I, II. Function Theory, The Wadsworth & Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1990. |
[43] |
L. Hörmander, The Analysis of Linear Partial Differential Operators. II. Differential Operators with Constant Coefficients, Reprint of the 1983 original, Classics in Mathematics, Springer-Verlag, Berlin, 2005. |
[44] |
H. W. E. Jung, Über ganze birationale Transformationen der Ebene, J. Reine Angew. Math., 184 (1942), 161-174. |
[45] |
A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, With a supplementary chapter by Katok and L. Mendoza, Encyclopedia of Mathematics and its Applications, 54, Cambridge University Press, Cambridge, 1995.
doi: 10.1017/CBO9780511809187. |
[46] |
A. G. Khovanskii, The geometry of convex polyhedra and algebraic geometry, Uspehi Mat. Nauk., 34 (1979), 160-161. |
[47] |
S. Kobayashi, Hyperbolic Complex Spaces, Grundlehren der Mathematischen Wissenschaften, 318, Springer-Verlag, Berlin, 1998.
doi: 10.1007/978-3-662-03582-5. |
[48] |
P. Lelong, Fonctions Plurisousharmoniques Et Formes Différentielles Positives, Gordon & Breach, Paris-London-New York (Distributed by Dunod éditeur, Paris), 1968. |
[49] |
C. T. McMullen, Dynamics on blowups of the projective plane, Publ. Math. Inst. Hautes Études Sci., 105 (2007), 49-89.
doi: 10.1007/s10240-007-0004-x. |
[50] |
M. McQuillan, Diophantine approximations and foliations, Inst. Hautes Études Sci. Publ. Math., 87 (1998), 121-174. |
[51] |
A. Moncet, Géométrie et dynamique sur les surfaces algébriques réelles, Ph.D thesis, arXiv:1207.0390, 2012. |
[52] |
R. Nevanlinna, Analytic Functions, Translated from the second German edition by P. Emig, {Die Grundlehren der mathematischen Wissenschaften}, Band 162 Springer-Verlag, New York-Berlin, 1970. |
[53] |
K. Oguiso, A remark on dynamical degrees of automorphisms of hyperkähler manifolds, Manuscripta Math., 130 (2009), 101-111.
doi: 10.1007/s00229-009-0271-6. |
[54] |
I. P. Shestakov and U. U. Umirbaev, The tame and the wild automorphisms of polynomial rings in three variables, J. Amer. Math. Soc., 17 (2004), 197-227.
doi: 10.1090/S0894-0347-03-00440-5. |
[55] |
N. Sibony, Dynamique des applications rationnelles de $\mathbbP^k$, in Dynamique et Géométrie Complexes (Lyon, 1997), Panoramas et Synthèses, 8, Soc. Math. France, Paris, 1999, ix-x, xi-xii, 97-185. |
[56] |
T. Uehara, Rational surface automorphisms with positive entropy, arXiv:1009.2143, 2010. |
[57] |
C. Voisin, Théorie de Hodge et Géométrie Algébrique Complexe, Cours Spécialisés, 10, Société Mathématique de France, Paris, 2002.
doi: 10.1017/CBO9780511615344. |
[58] |
J. Taflin, Equidistribution speed towards the Green current for endomorphisms of $ \mathbbP^k$, Adv. Math., 227 (2011), 2059-2081.
doi: 10.1016/j.aim.2011.04.010. |
[59] |
B. Teissier, Du théorème de l'index de Hodge aux inégalités isopérimétriques, C. R. Acad. Sci. Paris Sér. A-B, 288 (1979), A287-A289. |
[60] |
V. A. Timorin, Mixed Hodge-Riemann bilinear relations in a linear context, Funktsional. Anal. i Prilozhen., 32 (1998), 63-68, 96; translation in Funct. Anal. Appl., 32 (1998), 268-272.
doi: 10.1007/BF02463209. |
[61] |
S.-T. Yau, On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation. I, Comm. Pure Appl. Math., 31 (1978), 339-411.
doi: 10.1002/cpa.3160310304. |
[62] |
Y. Yomdin, Volume growth and entropy, Israel J. Math., 57 (1987), 285-300.
doi: 10.1007/BF02766215. |
[1] |
Fernando Lenarduzzi. Recoding the classical Hénon-Devaney map. Discrete and Continuous Dynamical Systems, 2020, 40 (7) : 4073-4092. doi: 10.3934/dcds.2020172 |
[2] |
Yu-Hao Liang, Wan-Rou Wu, Jonq Juang. Fastest synchronized network and synchrony on the Julia set of complex-valued coupled map lattices. Discrete and Continuous Dynamical Systems - B, 2016, 21 (1) : 173-184. doi: 10.3934/dcdsb.2016.21.173 |
[3] |
François Berteloot, Tien-Cuong Dinh. The Mandelbrot set is the shadow of a Julia set. Discrete and Continuous Dynamical Systems, 2020, 40 (12) : 6611-6633. doi: 10.3934/dcds.2020262 |
[4] |
Luke G. Rogers, Alexander Teplyaev. Laplacians on the basilica Julia set. Communications on Pure and Applied Analysis, 2010, 9 (1) : 211-231. doi: 10.3934/cpaa.2010.9.211 |
[5] |
Chihiro Matsuoka, Koichi Hiraide. Special functions created by Borel-Laplace transform of Hénon map. Electronic Research Announcements, 2011, 18: 1-11. doi: 10.3934/era.2011.18.1 |
[6] |
Ming Zhao, Cuiping Li, Jinliang Wang, Zhaosheng Feng. Bifurcation analysis of the three-dimensional Hénon map. Discrete and Continuous Dynamical Systems - S, 2017, 10 (3) : 625-645. doi: 10.3934/dcdss.2017031 |
[7] |
Mads R. Bisgaard. Mather theory and symplectic rigidity. Journal of Modern Dynamics, 2019, 15: 165-207. doi: 10.3934/jmd.2019018 |
[8] |
Artem Dudko. Computability of the Julia set. Nonrecurrent critical orbits. Discrete and Continuous Dynamical Systems, 2014, 34 (7) : 2751-2778. doi: 10.3934/dcds.2014.34.2751 |
[9] |
James W. Cannon, Mark H. Meilstrup, Andreas Zastrow. The period set of a map from the Cantor set to itself. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 2667-2679. doi: 10.3934/dcds.2013.33.2667 |
[10] |
Christophe Dupont, Axel Rogue. On the regularity of the Green current for semi-extremal endomorphisms of $ \mathbb{P}^2 $. Discrete and Continuous Dynamical Systems, 2020, 40 (12) : 6767-6781. doi: 10.3934/dcds.2020163 |
[11] |
Koh Katagata. On a certain kind of polynomials of degree 4 with disconnected Julia set. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 975-987. doi: 10.3934/dcds.2008.20.975 |
[12] |
Volodymyr Nekrashevych. The Julia set of a post-critically finite endomorphism of $\mathbb{PC}^2$. Journal of Modern Dynamics, 2012, 6 (3) : 327-375. doi: 10.3934/jmd.2012.6.327 |
[13] |
Rich Stankewitz. Density of repelling fixed points in the Julia set of a rational or entire semigroup, II. Discrete and Continuous Dynamical Systems, 2012, 32 (7) : 2583-2589. doi: 10.3934/dcds.2012.32.2583 |
[14] |
Luis F. López, Yannick Sire. Rigidity results for nonlocal phase transitions in the Heisenberg group $\mathbb{H}$. Discrete and Continuous Dynamical Systems, 2014, 34 (6) : 2639-2656. doi: 10.3934/dcds.2014.34.2639 |
[15] |
Fredi Tröltzsch, Alberto Valli. Optimal voltage control of non-stationary eddy current problems. Mathematical Control and Related Fields, 2018, 8 (1) : 35-56. doi: 10.3934/mcrf.2018002 |
[16] |
Mark Comerford, Rich Stankewitz, Hiroki Sumi. Hereditarily non uniformly perfect non-autonomous Julia sets. Discrete and Continuous Dynamical Systems, 2020, 40 (1) : 33-46. doi: 10.3934/dcds.2020002 |
[17] |
Alexander Blokh, Lex Oversteegen, Vladlen Timorin. Non-degenerate locally connected models for plane continua and Julia sets. Discrete and Continuous Dynamical Systems, 2017, 37 (11) : 5781-5795. doi: 10.3934/dcds.2017251 |
[18] |
Mark Comerford. Non-autonomous Julia sets with measurable invariant sequences of line fields. Discrete and Continuous Dynamical Systems, 2013, 33 (2) : 629-642. doi: 10.3934/dcds.2013.33.629 |
[19] |
Anna Lisa Amadori. Global bifurcation for the Hénon problem. Communications on Pure and Applied Analysis, 2020, 19 (10) : 4797-4816. doi: 10.3934/cpaa.2020212 |
[20] |
C. R. Chen, S. J. Li. Semicontinuity of the solution set map to a set-valued weak vector variational inequality. Journal of Industrial and Management Optimization, 2007, 3 (3) : 519-528. doi: 10.3934/jimo.2007.3.519 |
2020 Impact Factor: 0.848
Tools
Metrics
Other articles
by authors
[Back to Top]