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Regularity and convergence rates for the Lyapunov exponents of linear cocycles
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Codimension-1 partially hyperbolic diffeomorphisms with a uniformly compact center foliation
The $C^{1+\alpha }$ hypothesis in Pesin Theory revisited
1. | Institut de Mathématiques de Bourgogne, Université de Bourgogne, Dijon 21004 |
2. | Laboratoire de Mathématiques d’Orsay CNRS - UMR 8628 Université Paris-Sud 11 Orsay 91405, France |
3. | FIRST, Aihara Innovative Mathematical Modelling Project, JST, Institute of Industrial Science, University of Tokyo, 4-6-1, Komaba, Meguro-ku, Tokyo 153-8505, Japan |
References:
[1] |
F. Abdenur, C. Bonatti and S. Crovisier, Nonuniform hyperbolicity for $C^1$-generic diffeomorphisms, Israel J. Math., 183 (2011), 1-60.
doi: 10.1007/s11856-011-0041-5. |
[2] |
F. Abdenur, C. Bonatti, S. Crovisier, L. Díaz and L. Wen, Periodic points and homoclinic classes, Erg. Th. Dyn. Sys., 27 (2007), 1-22.
doi: 10.1017/S0143385706000538. |
[3] |
C. Bonatti, Towards a global view of dynamical systems, for the $C^1$-topology, Erg. Th. Dyn. Sys., 31 (2011), 959-993.
doi: 10.1017/S0143385710000891. |
[4] |
C. Bonatti and S. Crovisier, Récurrence et généricité, Invent. Math., 158 (2004), 33-104.
doi: 10.1007/s00222-004-0368-1. |
[5] |
C. Bonatti, S. Crovisier, L. Díaz and N. Gourmelon, Internal perturbations of homoclinic classes: Non-domination, cycles, and self-replication, Erg. Th. Dyn. Sys., 33 (2013), 739-776.
doi: 10.1017/S0143385712000028. |
[6] |
C. Bonatti and L. Díaz, On maximal transitive sets of generic diffeomorphisms, Publ. Math. Inst. Hautes Études Sci., 96 (2002), 171-197.
doi: 10.1007/s10240-003-0008-0. |
[7] |
C. Bonatti, L. Díaz and M. Viana, Dynamics Beyond Uniform Hyperbolicity. A Global Geometric and Probabilistic Perspective, Encyclopaedia of Mathematical Sciences, 102, Mathematical Physics, III, Springer-Verlag, Berlin, 2004. |
[8] |
J. Buescu and I. Stewart, Liapunov stability and adding machines, Erg. Th. Dyn. Sys., 15 (1995), 271-290.
doi: 10.1017/S0143385700008373. |
[9] |
L. Barreira and C. Valls, Existence of stable manifolds for nonuniformly hyperbolic $C^1$ dynamics, Discrete Contin. Dyn. Syst., 16 (2006), 307-327.
doi: 10.3934/dcds.2006.16.307. |
[10] |
N. Gourmelon, Generation of homoclinic tangencies by $C^1$-perturbations, Discrete Contin. Dyn. Syst., 26 (2010), 1-42.
doi: 10.3934/dcds.2010.26.1. |
[11] |
N. Gourmelon, An isotopic perturbation lemma along periodic orbits,, , ().
|
[12] |
F. Ledrappier, Quelques propriétés des exposants caractéristiques, in École d'été de Probabilités de Saint-Flour, XII-1982, Lecture Notes in Math., 1097, Springer, Berlin, 1984, 305-396.
doi: 10.1007/BFb0099434. |
[13] |
R. Mañé, An ergodic closing lemma, Ann. of Math. (2), 116 (1982), 503-540.
doi: 10.2307/2007021. |
[14] |
L. Markus and K. Meyer, Periodic orbits and solenoids in generic Hamiltonian dynamical systems, Amer. J. Math., 102 (1980), 25-92.
doi: 10.2307/2374171. |
[15] |
Ja. B. Pesin, Families of invariant manifolds that correspond to nonzero characteristic exponents, Math. USSR-Izv., 10 (1976), 1261-1305. |
[16] |
C. Pugh, The $C^{1+\alpha }$ hypothesis in Pesin theory, Inst. Hautes Études Sci. Publ. Math., 59 (1984), 143-161. |
show all references
References:
[1] |
F. Abdenur, C. Bonatti and S. Crovisier, Nonuniform hyperbolicity for $C^1$-generic diffeomorphisms, Israel J. Math., 183 (2011), 1-60.
doi: 10.1007/s11856-011-0041-5. |
[2] |
F. Abdenur, C. Bonatti, S. Crovisier, L. Díaz and L. Wen, Periodic points and homoclinic classes, Erg. Th. Dyn. Sys., 27 (2007), 1-22.
doi: 10.1017/S0143385706000538. |
[3] |
C. Bonatti, Towards a global view of dynamical systems, for the $C^1$-topology, Erg. Th. Dyn. Sys., 31 (2011), 959-993.
doi: 10.1017/S0143385710000891. |
[4] |
C. Bonatti and S. Crovisier, Récurrence et généricité, Invent. Math., 158 (2004), 33-104.
doi: 10.1007/s00222-004-0368-1. |
[5] |
C. Bonatti, S. Crovisier, L. Díaz and N. Gourmelon, Internal perturbations of homoclinic classes: Non-domination, cycles, and self-replication, Erg. Th. Dyn. Sys., 33 (2013), 739-776.
doi: 10.1017/S0143385712000028. |
[6] |
C. Bonatti and L. Díaz, On maximal transitive sets of generic diffeomorphisms, Publ. Math. Inst. Hautes Études Sci., 96 (2002), 171-197.
doi: 10.1007/s10240-003-0008-0. |
[7] |
C. Bonatti, L. Díaz and M. Viana, Dynamics Beyond Uniform Hyperbolicity. A Global Geometric and Probabilistic Perspective, Encyclopaedia of Mathematical Sciences, 102, Mathematical Physics, III, Springer-Verlag, Berlin, 2004. |
[8] |
J. Buescu and I. Stewart, Liapunov stability and adding machines, Erg. Th. Dyn. Sys., 15 (1995), 271-290.
doi: 10.1017/S0143385700008373. |
[9] |
L. Barreira and C. Valls, Existence of stable manifolds for nonuniformly hyperbolic $C^1$ dynamics, Discrete Contin. Dyn. Syst., 16 (2006), 307-327.
doi: 10.3934/dcds.2006.16.307. |
[10] |
N. Gourmelon, Generation of homoclinic tangencies by $C^1$-perturbations, Discrete Contin. Dyn. Syst., 26 (2010), 1-42.
doi: 10.3934/dcds.2010.26.1. |
[11] |
N. Gourmelon, An isotopic perturbation lemma along periodic orbits,, , ().
|
[12] |
F. Ledrappier, Quelques propriétés des exposants caractéristiques, in École d'été de Probabilités de Saint-Flour, XII-1982, Lecture Notes in Math., 1097, Springer, Berlin, 1984, 305-396.
doi: 10.1007/BFb0099434. |
[13] |
R. Mañé, An ergodic closing lemma, Ann. of Math. (2), 116 (1982), 503-540.
doi: 10.2307/2007021. |
[14] |
L. Markus and K. Meyer, Periodic orbits and solenoids in generic Hamiltonian dynamical systems, Amer. J. Math., 102 (1980), 25-92.
doi: 10.2307/2374171. |
[15] |
Ja. B. Pesin, Families of invariant manifolds that correspond to nonzero characteristic exponents, Math. USSR-Izv., 10 (1976), 1261-1305. |
[16] |
C. Pugh, The $C^{1+\alpha }$ hypothesis in Pesin theory, Inst. Hautes Études Sci. Publ. Math., 59 (1984), 143-161. |
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