-
Previous Article
Non-algebraic attractors on $\mathbf{P}^k$
- DCDS Home
- This Issue
-
Next Article
Pisot family self-affine tilings, discrete spectrum, and the Meyer property
Approximations for Gibbs states of arbitrary Hölder potentials on hyperbolic folded sets
1. | Institute of Mathematics "Simion Stoilow" of the Romanian Academy, P.O Box 1-764, RO 014-700, Bucharest |
References:
[1] |
H. G. Bothe, Shift spaces and attractors in noninvertible horseshoes, Fundamenta Math., 152 (1997), 267-289. |
[2] |
R. Bowen, "Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms," Lecture Notes in Mathematics, 470, Springer-Verlag, Berlin, 1975. |
[3] |
A. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems," With a supplementary chapter by A. Katok and L. Mendoza, Encyclopedia of Mathematics and its Applications, 54, Cambridge Univ. Press, Cambridge, 1995. |
[4] |
R. Mane, "Ergodic Theory and Differentiable Dynamics," Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 8, Springer-Verlag, Berlin, 1987. |
[5] |
E. Mihailescu, Unstable directions and fractal dimensions for skew products with overlaps in fibers, Math. Zeitschrift, 2011.
doi: 10.1007/s00209-010-0761-y. |
[6] |
E. Mihailescu, Metric properties of some fractals and applications of inverse pressure, Math. Proceed. Cambridge Phil. Soc., 148 (2010), 553-572.
doi: 10.1017/S0305004109990326. |
[7] |
E. Mihailescu, On a class of stable conditional measures, Ergodic Th. and Dynam. Syst., 31 (2011), 1499-1515.
doi: 10.1017/S0143385710000477. |
[8] |
E. Mihailescu, Unstable manifolds and Hölder structures associated with noninvertible maps, Discrete and Cont. Dynam. Syst., 14 (2006), 419-446.
doi: 10.3934/dcds.2006.14.419. |
[9] |
E. Mihailescu, The set $K^-$ for hyperbolic non-invertible maps, Ergodic Th. and Dynam. Syst., 22 (2002), 873-887. |
[10] |
E. Mihailescu and M. Urbański, Transversal families of hyperbolic skew-products, Discrete and Cont. Dynam. Syst., 21 (2008), 907-928.
doi: 10.3934/dcds.2008.21.907. |
[11] |
M. Qian and Z. S. Zhang, Ergodic theory for Axiom A endomorphisms, Ergodic Th. and Dyn. Syst., 15 (1995), 161-174. |
[12] |
M. Qian and Z. Shu, SRB measures and Pesin's entropy formula for endomorphisms, Trans. Amer. Math. Soc., 354 (2002), 1453-1471.
doi: 10.1090/S0002-9947-01-02792-1. |
[13] |
D. Ruelle, The thermodynamic formalism for expanding maps, Commun. Math. Physics, 125 (1989), 239-262.
doi: 10.1007/BF01217908. |
[14] |
D. Ruelle, "Elements of Differentiable Dynamics and Bifurcation Theory," Academic Press, Inc., Boston, MA, 1989. |
[15] |
D. Ruelle, Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics, J. Statist. Phys., 95 (1999), 393-468.
doi: 10.1023/A:1004593915069. |
[16] |
Y. Sinaǐ, Gibbs measures in ergodic theory, Uspehi Mat. Nauk, 27 (1972), 21-64. |
[17] |
P. Walters, "An Introduction to Ergodic Theory," Graduate Texts in Mathematics, 79, Springer-Verlag, New York-Berlin, 1982. |
[18] |
M. Zhang, "Anosov Endomorphisms: Shift Equivalence and Shift-Equivalence Classes," Ph.D Thesis, Peking Univ., 1989. |
show all references
References:
[1] |
H. G. Bothe, Shift spaces and attractors in noninvertible horseshoes, Fundamenta Math., 152 (1997), 267-289. |
[2] |
R. Bowen, "Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms," Lecture Notes in Mathematics, 470, Springer-Verlag, Berlin, 1975. |
[3] |
A. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems," With a supplementary chapter by A. Katok and L. Mendoza, Encyclopedia of Mathematics and its Applications, 54, Cambridge Univ. Press, Cambridge, 1995. |
[4] |
R. Mane, "Ergodic Theory and Differentiable Dynamics," Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 8, Springer-Verlag, Berlin, 1987. |
[5] |
E. Mihailescu, Unstable directions and fractal dimensions for skew products with overlaps in fibers, Math. Zeitschrift, 2011.
doi: 10.1007/s00209-010-0761-y. |
[6] |
E. Mihailescu, Metric properties of some fractals and applications of inverse pressure, Math. Proceed. Cambridge Phil. Soc., 148 (2010), 553-572.
doi: 10.1017/S0305004109990326. |
[7] |
E. Mihailescu, On a class of stable conditional measures, Ergodic Th. and Dynam. Syst., 31 (2011), 1499-1515.
doi: 10.1017/S0143385710000477. |
[8] |
E. Mihailescu, Unstable manifolds and Hölder structures associated with noninvertible maps, Discrete and Cont. Dynam. Syst., 14 (2006), 419-446.
doi: 10.3934/dcds.2006.14.419. |
[9] |
E. Mihailescu, The set $K^-$ for hyperbolic non-invertible maps, Ergodic Th. and Dynam. Syst., 22 (2002), 873-887. |
[10] |
E. Mihailescu and M. Urbański, Transversal families of hyperbolic skew-products, Discrete and Cont. Dynam. Syst., 21 (2008), 907-928.
doi: 10.3934/dcds.2008.21.907. |
[11] |
M. Qian and Z. S. Zhang, Ergodic theory for Axiom A endomorphisms, Ergodic Th. and Dyn. Syst., 15 (1995), 161-174. |
[12] |
M. Qian and Z. Shu, SRB measures and Pesin's entropy formula for endomorphisms, Trans. Amer. Math. Soc., 354 (2002), 1453-1471.
doi: 10.1090/S0002-9947-01-02792-1. |
[13] |
D. Ruelle, The thermodynamic formalism for expanding maps, Commun. Math. Physics, 125 (1989), 239-262.
doi: 10.1007/BF01217908. |
[14] |
D. Ruelle, "Elements of Differentiable Dynamics and Bifurcation Theory," Academic Press, Inc., Boston, MA, 1989. |
[15] |
D. Ruelle, Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics, J. Statist. Phys., 95 (1999), 393-468.
doi: 10.1023/A:1004593915069. |
[16] |
Y. Sinaǐ, Gibbs measures in ergodic theory, Uspehi Mat. Nauk, 27 (1972), 21-64. |
[17] |
P. Walters, "An Introduction to Ergodic Theory," Graduate Texts in Mathematics, 79, Springer-Verlag, New York-Berlin, 1982. |
[18] |
M. Zhang, "Anosov Endomorphisms: Shift Equivalence and Shift-Equivalence Classes," Ph.D Thesis, Peking Univ., 1989. |
[1] |
Luis Barreira. Nonadditive thermodynamic formalism: Equilibrium and Gibbs measures. Discrete and Continuous Dynamical Systems, 2006, 16 (2) : 279-305. doi: 10.3934/dcds.2006.16.279 |
[2] |
Chris Good, Robin Knight, Brian Raines. Countable inverse limits of postcritical $w$-limit sets of unimodal maps. Discrete and Continuous Dynamical Systems, 2010, 27 (3) : 1059-1078. doi: 10.3934/dcds.2010.27.1059 |
[3] |
Gerhard Keller. Stability index, uncertainty exponent, and thermodynamic formalism for intermingled basins of chaotic attractors. Discrete and Continuous Dynamical Systems - S, 2017, 10 (2) : 313-334. doi: 10.3934/dcdss.2017015 |
[4] |
Eugen Mihailescu. Equilibrium measures, prehistories distributions and fractal dimensions for endomorphisms. Discrete and Continuous Dynamical Systems, 2012, 32 (7) : 2485-2502. doi: 10.3934/dcds.2012.32.2485 |
[5] |
Renaud Leplaideur. From local to global equilibrium states: Thermodynamic formalism via an inducing scheme. Electronic Research Announcements, 2014, 21: 72-79. doi: 10.3934/era.2014.21.72 |
[6] |
Marzie Zaj, Abbas Fakhari, Fatemeh Helen Ghane, Azam Ehsani. Physical measures for certain class of non-uniformly hyperbolic endomorphisms on the solid torus. Discrete and Continuous Dynamical Systems, 2018, 38 (4) : 1777-1807. doi: 10.3934/dcds.2018073 |
[7] |
Eugen Mihailescu. Applications of thermodynamic formalism in complex dynamics on $\mathbb{P}^2$. Discrete and Continuous Dynamical Systems, 2001, 7 (4) : 821-836. doi: 10.3934/dcds.2001.7.821 |
[8] |
Yakov Pesin, Samuel Senti. Equilibrium measures for maps with inducing schemes. Journal of Modern Dynamics, 2008, 2 (3) : 397-430. doi: 10.3934/jmd.2008.2.397 |
[9] |
Kurt Falk, Marc Kesseböhmer, Tobias Henrik Oertel-Jäger, Jens D. M. Rademacher, Tony Samuel. Preface: Diffusion on fractals and non-linear dynamics. Discrete and Continuous Dynamical Systems - S, 2017, 10 (2) : i-iv. doi: 10.3934/dcdss.201702i |
[10] |
Cezar Joiţa, William O. Nowell, Pantelimon Stănică. Chaotic dynamics of some rational maps. Discrete and Continuous Dynamical Systems, 2005, 12 (2) : 363-375. doi: 10.3934/dcds.2005.12.363 |
[11] |
Zhihong Xia. Hyperbolic invariant sets with positive measures. Discrete and Continuous Dynamical Systems, 2006, 15 (3) : 811-818. doi: 10.3934/dcds.2006.15.811 |
[12] |
Vítor Araújo, Ali Tahzibi. Physical measures at the boundary of hyperbolic maps. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 849-876. doi: 10.3934/dcds.2008.20.849 |
[13] |
Imen Bhouri, Houssem Tlili. On the multifractal formalism for Bernoulli products of invertible matrices. Discrete and Continuous Dynamical Systems, 2009, 24 (4) : 1129-1145. doi: 10.3934/dcds.2009.24.1129 |
[14] |
Evelyn Sander. Hyperbolic sets for noninvertible maps and relations. Discrete and Continuous Dynamical Systems, 1999, 5 (2) : 339-357. doi: 10.3934/dcds.1999.5.339 |
[15] |
Xueting Tian, Paulo Varandas. Topological entropy of level sets of empirical measures for non-uniformly expanding maps. Discrete and Continuous Dynamical Systems, 2017, 37 (10) : 5407-5431. doi: 10.3934/dcds.2017235 |
[16] |
Vaughn Climenhaga. A note on two approaches to the thermodynamic formalism. Discrete and Continuous Dynamical Systems, 2010, 27 (3) : 995-1005. doi: 10.3934/dcds.2010.27.995 |
[17] |
Vaughn Climenhaga, Yakov Pesin, Agnieszka Zelerowicz. Equilibrium measures for some partially hyperbolic systems. Journal of Modern Dynamics, 2020, 16: 155-205. doi: 10.3934/jmd.2020006 |
[18] |
Anatole Katok. Hyperbolic measures and commuting maps in low dimension. Discrete and Continuous Dynamical Systems, 1996, 2 (3) : 397-411. doi: 10.3934/dcds.1996.2.397 |
[19] |
Tifei Qian, Zhihong Xia. Heteroclinic orbits and chaotic invariant sets for monotone twist maps. Discrete and Continuous Dynamical Systems, 2003, 9 (1) : 69-95. doi: 10.3934/dcds.2003.9.69 |
[20] |
Michael Jakobson, Lucia D. Simonelli. Countable Markov partitions suitable for thermodynamic formalism. Journal of Modern Dynamics, 2018, 13: 199-219. doi: 10.3934/jmd.2018018 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]