-
Previous Article
Genericity of nonuniform hyperbolicity in dimension 3
- JMD Home
- This Issue
-
Next Article
Reducibility of quasiperiodic cocycles under a Brjuno-Rüssmann arithmetical condition
Hölder foliations, revisited
1. | Department ofMathematics, University of Chicago, 5734 S. University Ave., Chicago, Illinois 60637, United States, United States |
2. | CONICET, IMAS, Universidad de Buenos Aires, Buenos Aires, Argentina |
References:
[1] |
D. V. Anosov, Geodesic flows on closed Riemann manifolds with negative curvature, (Russian), Trudy Mat. Inst. Stecklov., 90 (1967), 209 pp. |
[2] |
D. Bohnet, "Partially Hyperbolic Systems with a Compact Center Foliation with Finite Holonomy," Ph.D Thesis, Universität Hamburg, 2011. |
[3] |
C. Bonatti and A. Wilkinson, Transitive partially hyperbolic diffeomorphisms on 3-manifolds, Topology, 44 (2005), 475-508.
doi: 10.1016/j.top.2004.10.009. |
[4] |
K. Burns and A. Wilkinson, Dynamical coherence and center bunching, Discrete Contin. Dyn. Syst., 22 (2008), 89-100.
doi: 10.3934/dcds.2008.22.89. |
[5] |
P. Carrasco, "Compact Dynamical Foliations," Ph.D Thesis, University of Toronto, Canada, 2010. |
[6] |
J. Cheeger and D. Ebin, "Comparison Theorems in Riemannian Geometry," North-Holland Mathematical Library, Vol. 9, North Holland Publishing Co., Amsterdam-Oxford, American Elsevier Publishing, Co., Inc., New York, 1975. |
[7] | |
[8] |
D. Damjanović and A. Katok, Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic $\mathbb R^k$ actions, Discrete Contin. Dyn. Syst., 13 (2005), 985-1005.
doi: 10.3934/dcds.2005.13.985. |
[9] |
D. Damjanović and A. Katok, Local rigidity of partially hyperbolic actions. II. The geometric method and restrictions of Weyl chamber flows on $SL(n,\mathbbR)$/$Gamma$, Int. Math. Res. Not. IMRN, 2011, 4405-4430. |
[10] |
D. Epstein, Foliations with all leaves compact, Ann. Inst. Fourier (Grenoble), 26 (1976), 265-282.
doi: 10.5802/aif.607. |
[11] |
A. Hammerlindl, Quasi-isometry and plaque expansiveness, Canadian Mathematical Bulletin, 54 (2011), 676-679.
doi: 10.4153/CMB-2011-024-7. |
[12] |
B. Hasselblatt, Regularity of the Anosov splitting. II, Ergodic Theory Dynam. Systems, 17 (1997), 169-172.
doi: 10.1017/S0143385797069757. |
[13] |
B. Hasselblatt and A. Wilkinson, Prevalence of non-Lipschitz Anosov foliations, Ergodic Theory Dynam. Systems, 19 (1999), 643-656.
doi: 10.1017/S0143385799133868. |
[14] |
F. Rodriguez Hertz, M. A. Rodriguez Hertz and R. Ures, A survey of partially hyperbolic dynamics, in "Partially Hyperbolic Dynamics, Laminations, and Teichmüller Flow," Fields Inst. Commun., 51, Amer. Math. Soc., Providence, RI, (2007), 35-87. |
[15] |
M. Hirsch, C. Pugh and M. Shub, "Invariant Manifolds," Lecture Notes in Mathematics, 583, Springer-Verlag, Berlin-New York, 1977. |
[16] |
Y. Ilyashenko and A. Negut, Hölder properties of perturbed skew products and Fubini regained, preprint. |
[17] |
A. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems," With a supplementary chapter by Katok and Leonardo Mendoza, Encyclopedia of Mathematics and its Applications, 54, Cambridge University Press, Cambridge, 1995. |
[18] |
V. Niţică and A. Török, Cohomology of dynamical systems and rigidity of partially hyperbolic actions of higher-rank lattices, Duke Math. J., 79 (1995), 751-810. |
[19] |
C. Pugh, M. Shub and A. Wilkinson, Hölder foliations, Duke Math. J., 86 (1997), 517-546.
doi: 10.1215/S0012-7094-97-08616-6. |
[20] |
C. Pugh, M. Shub and A. Wilkinson, Correction to: "Hölder foliations," Duke Math. J., 105 (2000), 105-106. |
[21] |
J. Schmeling and Ra. Siegmund-Schultze, Hölder-continuity of the holonomy maps for hyperbolic sets, in "Ergodic Theory and Related Topics, III" (Güstrow, 1990), Lecture Notes in Math., 1514, Springer, Berlin, (1992), 174-191. |
[22] |
M. Shub, "Global Stability of Dynamical Systems," With the collaboration of Albert Fathi and Rémi Langevin, Translated from the French by Joseph Christy, Springer-Verlag, New York, 1987. |
[23] |
A. Wilkinson, Stable ergodicity of the time-one map of a geodesic flow, Ergod. Th. & Dynam. Sys., 18 (1998), 1545-1587. |
[24] |
A. Wilkinson, The cohomological equation for partially hyperbolic diffeomorphisms, preprint, 2008. |
show all references
References:
[1] |
D. V. Anosov, Geodesic flows on closed Riemann manifolds with negative curvature, (Russian), Trudy Mat. Inst. Stecklov., 90 (1967), 209 pp. |
[2] |
D. Bohnet, "Partially Hyperbolic Systems with a Compact Center Foliation with Finite Holonomy," Ph.D Thesis, Universität Hamburg, 2011. |
[3] |
C. Bonatti and A. Wilkinson, Transitive partially hyperbolic diffeomorphisms on 3-manifolds, Topology, 44 (2005), 475-508.
doi: 10.1016/j.top.2004.10.009. |
[4] |
K. Burns and A. Wilkinson, Dynamical coherence and center bunching, Discrete Contin. Dyn. Syst., 22 (2008), 89-100.
doi: 10.3934/dcds.2008.22.89. |
[5] |
P. Carrasco, "Compact Dynamical Foliations," Ph.D Thesis, University of Toronto, Canada, 2010. |
[6] |
J. Cheeger and D. Ebin, "Comparison Theorems in Riemannian Geometry," North-Holland Mathematical Library, Vol. 9, North Holland Publishing Co., Amsterdam-Oxford, American Elsevier Publishing, Co., Inc., New York, 1975. |
[7] | |
[8] |
D. Damjanović and A. Katok, Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic $\mathbb R^k$ actions, Discrete Contin. Dyn. Syst., 13 (2005), 985-1005.
doi: 10.3934/dcds.2005.13.985. |
[9] |
D. Damjanović and A. Katok, Local rigidity of partially hyperbolic actions. II. The geometric method and restrictions of Weyl chamber flows on $SL(n,\mathbbR)$/$Gamma$, Int. Math. Res. Not. IMRN, 2011, 4405-4430. |
[10] |
D. Epstein, Foliations with all leaves compact, Ann. Inst. Fourier (Grenoble), 26 (1976), 265-282.
doi: 10.5802/aif.607. |
[11] |
A. Hammerlindl, Quasi-isometry and plaque expansiveness, Canadian Mathematical Bulletin, 54 (2011), 676-679.
doi: 10.4153/CMB-2011-024-7. |
[12] |
B. Hasselblatt, Regularity of the Anosov splitting. II, Ergodic Theory Dynam. Systems, 17 (1997), 169-172.
doi: 10.1017/S0143385797069757. |
[13] |
B. Hasselblatt and A. Wilkinson, Prevalence of non-Lipschitz Anosov foliations, Ergodic Theory Dynam. Systems, 19 (1999), 643-656.
doi: 10.1017/S0143385799133868. |
[14] |
F. Rodriguez Hertz, M. A. Rodriguez Hertz and R. Ures, A survey of partially hyperbolic dynamics, in "Partially Hyperbolic Dynamics, Laminations, and Teichmüller Flow," Fields Inst. Commun., 51, Amer. Math. Soc., Providence, RI, (2007), 35-87. |
[15] |
M. Hirsch, C. Pugh and M. Shub, "Invariant Manifolds," Lecture Notes in Mathematics, 583, Springer-Verlag, Berlin-New York, 1977. |
[16] |
Y. Ilyashenko and A. Negut, Hölder properties of perturbed skew products and Fubini regained, preprint. |
[17] |
A. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems," With a supplementary chapter by Katok and Leonardo Mendoza, Encyclopedia of Mathematics and its Applications, 54, Cambridge University Press, Cambridge, 1995. |
[18] |
V. Niţică and A. Török, Cohomology of dynamical systems and rigidity of partially hyperbolic actions of higher-rank lattices, Duke Math. J., 79 (1995), 751-810. |
[19] |
C. Pugh, M. Shub and A. Wilkinson, Hölder foliations, Duke Math. J., 86 (1997), 517-546.
doi: 10.1215/S0012-7094-97-08616-6. |
[20] |
C. Pugh, M. Shub and A. Wilkinson, Correction to: "Hölder foliations," Duke Math. J., 105 (2000), 105-106. |
[21] |
J. Schmeling and Ra. Siegmund-Schultze, Hölder-continuity of the holonomy maps for hyperbolic sets, in "Ergodic Theory and Related Topics, III" (Güstrow, 1990), Lecture Notes in Math., 1514, Springer, Berlin, (1992), 174-191. |
[22] |
M. Shub, "Global Stability of Dynamical Systems," With the collaboration of Albert Fathi and Rémi Langevin, Translated from the French by Joseph Christy, Springer-Verlag, New York, 1987. |
[23] |
A. Wilkinson, Stable ergodicity of the time-one map of a geodesic flow, Ergod. Th. & Dynam. Sys., 18 (1998), 1545-1587. |
[24] |
A. Wilkinson, The cohomological equation for partially hyperbolic diffeomorphisms, preprint, 2008. |
[1] |
Rafael Potrie. Partial hyperbolicity and foliations in $\mathbb{T}^3$. Journal of Modern Dynamics, 2015, 9: 81-121. doi: 10.3934/jmd.2015.9.81 |
[2] |
Boris Hasselblatt. Critical regularity of invariant foliations. Discrete and Continuous Dynamical Systems, 2002, 8 (4) : 931-937. doi: 10.3934/dcds.2002.8.931 |
[3] |
Zhongkai Guo. Invariant foliations for stochastic partial differential equations with dynamic boundary conditions. Discrete and Continuous Dynamical Systems, 2015, 35 (11) : 5203-5219. doi: 10.3934/dcds.2015.35.5203 |
[4] |
Sergey Kryzhevich, Sergey Tikhomirov. Partial hyperbolicity and central shadowing. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 2901-2909. doi: 10.3934/dcds.2013.33.2901 |
[5] |
Ji Li, Kening Lu, Peter W. Bates. Invariant foliations for random dynamical systems. Discrete and Continuous Dynamical Systems, 2014, 34 (9) : 3639-3666. doi: 10.3934/dcds.2014.34.3639 |
[6] |
Paweł Lubowiecki, Henryk Żołądek. The Hess-Appelrot system. I. Invariant torus and its normal hyperbolicity. Journal of Geometric Mechanics, 2012, 4 (4) : 443-467. doi: 10.3934/jgm.2012.4.443 |
[7] |
Andy Hammerlindl, Jana Rodriguez Hertz, Raúl Ures. Ergodicity and partial hyperbolicity on Seifert manifolds. Journal of Modern Dynamics, 2020, 0: 331-348. doi: 10.3934/jmd.2020012 |
[8] |
Federico Rodriguez Hertz, María Alejandra Rodriguez Hertz, Raúl Ures. Partial hyperbolicity and ergodicity in dimension three. Journal of Modern Dynamics, 2008, 2 (2) : 187-208. doi: 10.3934/jmd.2008.2.187 |
[9] |
Jérôme Buzzi, Todd Fisher. Entropic stability beyond partial hyperbolicity. Journal of Modern Dynamics, 2013, 7 (4) : 527-552. doi: 10.3934/jmd.2013.7.527 |
[10] |
Yakov Pesin. On the work of Dolgopyat on partial and nonuniform hyperbolicity. Journal of Modern Dynamics, 2010, 4 (2) : 227-241. doi: 10.3934/jmd.2010.4.227 |
[11] |
Andy Hammerlindl. Partial hyperbolicity on 3-dimensional nilmanifolds. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 3641-3669. doi: 10.3934/dcds.2013.33.3641 |
[12] |
Eleonora Catsigeras, Xueting Tian. Dominated splitting, partial hyperbolicity and positive entropy. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 4739-4759. doi: 10.3934/dcds.2016006 |
[13] |
Marcin Mazur, Jacek Tabor, Piotr Kościelniak. Semi-hyperbolicity and hyperbolicity. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 1029-1038. doi: 10.3934/dcds.2008.20.1029 |
[14] |
Luis Barreira, Claudia Valls. Regularity of center manifolds under nonuniform hyperbolicity. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 55-76. doi: 10.3934/dcds.2011.30.55 |
[15] |
Jun Shen, Kening Lu, Bixiang Wang. Invariant manifolds and foliations for random differential equations driven by colored noise. Discrete and Continuous Dynamical Systems, 2020, 40 (11) : 6201-6246. doi: 10.3934/dcds.2020276 |
[16] |
Marcin Mazur, Jacek Tabor. Computational hyperbolicity. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 1175-1189. doi: 10.3934/dcds.2011.29.1175 |
[17] |
Boris Hasselblatt, Yakov Pesin, Jörg Schmeling. Pointwise hyperbolicity implies uniform hyperbolicity. Discrete and Continuous Dynamical Systems, 2014, 34 (7) : 2819-2827. doi: 10.3934/dcds.2014.34.2819 |
[18] |
Boris Kalinin, Anatole Katok. Measure rigidity beyond uniform hyperbolicity: invariant measures for cartan actions on tori. Journal of Modern Dynamics, 2007, 1 (1) : 123-146. doi: 10.3934/jmd.2007.1.123 |
[19] |
Gabriel Ponce, Ali Tahzibi, Régis Varão. Minimal yet measurable foliations. Journal of Modern Dynamics, 2014, 8 (1) : 93-107. doi: 10.3934/jmd.2014.8.93 |
[20] |
Radu Saghin. Note on homology of expanding foliations. Discrete and Continuous Dynamical Systems - S, 2009, 2 (2) : 349-360. doi: 10.3934/dcdss.2009.2.349 |
2021 Impact Factor: 0.641
Tools
Metrics
Other articles
by authors
[Back to Top]