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Center specification property and entropy for partially hyperbolic diffeomorphisms
1. | College of Mathematics and Information Science, and Hebei Key Laboratory of Computational Mathematics and Applications, Hebei Normal University, Shijiazhuang, 050024, China |
References:
[1] |
L. Barreira and Y. Pesin, Nonuniform Hyperbolicity, Cambridge University Press, Cambridge, 2007.
doi: 10.1017/CBO9781107326026. |
[2] |
D. Bohnet, Codimension-1 partially hyperbolic diffeomorphisms with a uniformly compact center foliation, Journal of Modern Dynamics, 7 (2013), 565-604.
doi: 10.3934/jmd.2013.7.565. |
[3] |
C. Bonatti and D. Bohnet, Partially hyperbolic diffeomorphisms with uniformly compact center foliations: the quotient dynamics, to appear in Ergodic Theory Dynam. Systems, arXiv:1210.2835. |
[4] |
C. Bonatti, L. Diaz and M. Viana, Dynamics Beyond Uniform Hyperbolicity: A Global Geometric and Probabilistic Perspective, Encyclopaedia Math. Sci., 102, Springer, Berlin, 2005. |
[5] |
R. Bowen, Periodic points and measures for Axiom A diffeomorphisms, Trans. Amer. Math., 154 (1971), 377-397. |
[6] |
M. Brin and J. Pesin, Partially hyperbolic dynamical systems, Izv. Akad. Nauk SSSR Ser. Mat., 38 (1974), 170-212.
doi: 10.1070/IM1974v008n01ABEH002101. |
[7] |
P. D. Carrasco, Compact Dynamical Foliations, Ph.D thesis, University of Toronto, 2011. |
[8] |
P. D. Carrasco, Compact dynamical foliations, to appear in Ergodic Theory Dynam. Systems, arXiv:1105.0052. |
[9] |
F. Hertz, J. Hertz and R. Ures, Partially Hyperbolic Dynamics, $28^0$ Coloquio Brasileiro de Matematica, IMPA Mathematical Publications, IMPA-Rio de Janeiro, 2011. |
[10] |
M. Hirsch, C. Pugh and M. Shub, Invariant Manifolds, Lect. Notes in Math. 583, Springer, New York, 1977. |
[11] |
H. Hu, Y. Zhou and Y. Zhu, Quasi-shadowing for partially hyperbolic diffeomorphisms, Ergodic Theory Dynam. Systems, 35 (2015), 412-430.
doi: 10.1017/etds.2014.126. |
[12] |
H. Hu, Y. Zhou and Y. Zhu, Quasi-shadowing and quasi-stability for dynamically coherent partially hyperbolic diffeomorphisms, arXiv:1405.0081. |
[13] |
A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, Cambridge, 1995.
doi: 10.1017/CBO9780511809187. |
[14] |
S. Kryzhevich and S. Tikhomirov, Partial hyperbolicity and central shadowing, Discrete Continuous Dynam. Systems, 33 (2013), 2901-2909.
doi: 10.3934/dcds.2013.33.2901. |
[15] |
Y. Pesin, Lectures on Partial Hyperbolicity and Stable Ergodicity, Zurich Lectures in Advanced Mathematics. European Math. Soc., Zurich, 2004.
doi: 10.4171/003. |
[16] |
C. Pugh, M. Shub and A. Wilkinson, Holder foliations, revisited, J. Modern Dyn., 6 (2012), 79-120.
doi: 10.3934/jmd.2012.6.79. |
[17] |
P. Walters, An Introduction to Ergodic Theory, Springer, New York, 1982. |
show all references
References:
[1] |
L. Barreira and Y. Pesin, Nonuniform Hyperbolicity, Cambridge University Press, Cambridge, 2007.
doi: 10.1017/CBO9781107326026. |
[2] |
D. Bohnet, Codimension-1 partially hyperbolic diffeomorphisms with a uniformly compact center foliation, Journal of Modern Dynamics, 7 (2013), 565-604.
doi: 10.3934/jmd.2013.7.565. |
[3] |
C. Bonatti and D. Bohnet, Partially hyperbolic diffeomorphisms with uniformly compact center foliations: the quotient dynamics, to appear in Ergodic Theory Dynam. Systems, arXiv:1210.2835. |
[4] |
C. Bonatti, L. Diaz and M. Viana, Dynamics Beyond Uniform Hyperbolicity: A Global Geometric and Probabilistic Perspective, Encyclopaedia Math. Sci., 102, Springer, Berlin, 2005. |
[5] |
R. Bowen, Periodic points and measures for Axiom A diffeomorphisms, Trans. Amer. Math., 154 (1971), 377-397. |
[6] |
M. Brin and J. Pesin, Partially hyperbolic dynamical systems, Izv. Akad. Nauk SSSR Ser. Mat., 38 (1974), 170-212.
doi: 10.1070/IM1974v008n01ABEH002101. |
[7] |
P. D. Carrasco, Compact Dynamical Foliations, Ph.D thesis, University of Toronto, 2011. |
[8] |
P. D. Carrasco, Compact dynamical foliations, to appear in Ergodic Theory Dynam. Systems, arXiv:1105.0052. |
[9] |
F. Hertz, J. Hertz and R. Ures, Partially Hyperbolic Dynamics, $28^0$ Coloquio Brasileiro de Matematica, IMPA Mathematical Publications, IMPA-Rio de Janeiro, 2011. |
[10] |
M. Hirsch, C. Pugh and M. Shub, Invariant Manifolds, Lect. Notes in Math. 583, Springer, New York, 1977. |
[11] |
H. Hu, Y. Zhou and Y. Zhu, Quasi-shadowing for partially hyperbolic diffeomorphisms, Ergodic Theory Dynam. Systems, 35 (2015), 412-430.
doi: 10.1017/etds.2014.126. |
[12] |
H. Hu, Y. Zhou and Y. Zhu, Quasi-shadowing and quasi-stability for dynamically coherent partially hyperbolic diffeomorphisms, arXiv:1405.0081. |
[13] |
A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, Cambridge, 1995.
doi: 10.1017/CBO9780511809187. |
[14] |
S. Kryzhevich and S. Tikhomirov, Partial hyperbolicity and central shadowing, Discrete Continuous Dynam. Systems, 33 (2013), 2901-2909.
doi: 10.3934/dcds.2013.33.2901. |
[15] |
Y. Pesin, Lectures on Partial Hyperbolicity and Stable Ergodicity, Zurich Lectures in Advanced Mathematics. European Math. Soc., Zurich, 2004.
doi: 10.4171/003. |
[16] |
C. Pugh, M. Shub and A. Wilkinson, Holder foliations, revisited, J. Modern Dyn., 6 (2012), 79-120.
doi: 10.3934/jmd.2012.6.79. |
[17] |
P. Walters, An Introduction to Ergodic Theory, Springer, New York, 1982. |
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