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Hyperbolic periodic points for chain hyperbolic homoclinic classes
1. | LMAM, School of Mathematical Sciences, Peking University, Beijing 100871 |
2. | School of Mathematical Sciences, Peking University, Beijing, 100871 |
References:
[1] |
R. Bowen, Periodic points and measures for Axiom a diffeomorphisms, Trans. Amer. Math. Soci., 154 (1971), 377-397. |
[2] |
Y. M. Chung and M. Hirayama, Topological entropy and periodic orbits of saddle type for surface diffeomorphisms, Hiroshima Math. J., 33 (2003), 189-195. |
[3] |
S. Crovisier, Partially hyperbolicity far from homoclinic bifurcations, Advances in Math., 226 (2011), 673-726.
doi: 10.1016/j.aim.2010.07.013. |
[4] |
S. Crovisier and E. Pujals, Essential hyperbolicity and homoclinic bifurcations: A dichotomy phenomenon/mechanism for diffeomorphisms, Invent. Math., 201 (2015), 385-517.
doi: 10.1007/s00222-014-0553-9. |
[5] |
M. Hirsch, C. Pugh and M. Shub, Invariant Manifolds, Lecture Notes in Mathematics, 583, springer Verlag, Berlin, 1977. |
[6] |
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. |
[7] |
A. Katok, Lyapunov exponents, entropy and periodic orbits for diffeomorphisms, Pub. Math. de l'Institut des Hautes Études Scientifiques, 51 (1980), 137-173. |
[8] |
S. Kryzhevich and S. Tikhomirov, Partial hyperbolicity and central shadowing, Discrete Contin. Dyn. Sys., 33 (2013), 2901-2909.
doi: 10.3934/dcds.2013.33.2901. |
[9] |
G. Liao, M. Viana and J. Yang, The Entropy Conjecture for Diffeomorphisms away from Tangencies, J. Eur. Math. Soc., 15 (2013), 2043-2060.
doi: 10.4171/JEMS/413. |
[10] |
J. Palis, A global view of dynamics and a conjecture on the denseness of finitude of attractors, Géométrie Complexe et Systèmes Dynamiques, Orsay, France, 261 (2000), 335-347. |
[11] |
J. Palis, A global perspective for non-conservative dynamics, Ann. Inst. H. Poincaré Anal. Non Linéaire, 22 (2005), 485-507.
doi: 10.1016/j.anihpc.2005.01.001. |
[12] |
V. Pliss, On a conjecture of Smale, Diff. Uravnenija, 8 (1972), 268-282. |
[13] |
K. Sigmund, Generic properties of invariant measures for Axiom A diffeomorphisms, Invent. Math., 11 (1970), 99-109.
doi: 10.1007/BF01404606. |
show all references
References:
[1] |
R. Bowen, Periodic points and measures for Axiom a diffeomorphisms, Trans. Amer. Math. Soci., 154 (1971), 377-397. |
[2] |
Y. M. Chung and M. Hirayama, Topological entropy and periodic orbits of saddle type for surface diffeomorphisms, Hiroshima Math. J., 33 (2003), 189-195. |
[3] |
S. Crovisier, Partially hyperbolicity far from homoclinic bifurcations, Advances in Math., 226 (2011), 673-726.
doi: 10.1016/j.aim.2010.07.013. |
[4] |
S. Crovisier and E. Pujals, Essential hyperbolicity and homoclinic bifurcations: A dichotomy phenomenon/mechanism for diffeomorphisms, Invent. Math., 201 (2015), 385-517.
doi: 10.1007/s00222-014-0553-9. |
[5] |
M. Hirsch, C. Pugh and M. Shub, Invariant Manifolds, Lecture Notes in Mathematics, 583, springer Verlag, Berlin, 1977. |
[6] |
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. |
[7] |
A. Katok, Lyapunov exponents, entropy and periodic orbits for diffeomorphisms, Pub. Math. de l'Institut des Hautes Études Scientifiques, 51 (1980), 137-173. |
[8] |
S. Kryzhevich and S. Tikhomirov, Partial hyperbolicity and central shadowing, Discrete Contin. Dyn. Sys., 33 (2013), 2901-2909.
doi: 10.3934/dcds.2013.33.2901. |
[9] |
G. Liao, M. Viana and J. Yang, The Entropy Conjecture for Diffeomorphisms away from Tangencies, J. Eur. Math. Soc., 15 (2013), 2043-2060.
doi: 10.4171/JEMS/413. |
[10] |
J. Palis, A global view of dynamics and a conjecture on the denseness of finitude of attractors, Géométrie Complexe et Systèmes Dynamiques, Orsay, France, 261 (2000), 335-347. |
[11] |
J. Palis, A global perspective for non-conservative dynamics, Ann. Inst. H. Poincaré Anal. Non Linéaire, 22 (2005), 485-507.
doi: 10.1016/j.anihpc.2005.01.001. |
[12] |
V. Pliss, On a conjecture of Smale, Diff. Uravnenija, 8 (1972), 268-282. |
[13] |
K. Sigmund, Generic properties of invariant measures for Axiom A diffeomorphisms, Invent. Math., 11 (1970), 99-109.
doi: 10.1007/BF01404606. |
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