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Modulation of uniform motion in diatomic Frenkel-Kontorova model
Volume growth and entropy for $C^1$ partially hyperbolic diffeomorphisms
1. | Instituto de Matemáticas, Pontifícia Universidad Católica de Valparaíso, Blanco Viel 596, Cerro Barón, Valparaíso, Chile |
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] |
K. Burns and A. Wilkinson, On the ergodicity of partially hyperbolic systems, Ann. of Math. (2), 171 (2010), 451-489.
doi: 10.4007/annals.2010.171.451. |
[3] |
N. Gourmelon, Adapted metrics for dominated splittings, Erg. Th. Dyn. Syst., 27 (2007), 1839-1849.
doi: 10.1017/S0143385707000272. |
[4] |
Y. Hua, R. Saghin and Z. Xia, Topological entropy and partially hyperbolic diffeomorphisms, Erg. Th. Dynam. Syst., 28 (2008), 843-862.
doi: 10.1017/S0143385707000405. |
[5] |
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 Univ. Press, Cambridge, 1995. |
[6] |
O. Kozlovski, An integral formula for topological entropy of $C^{\infty}$ maps, Erg. Th. Dyn. Sys., 18 (1998), 405-424.
doi: 10.1017/S0143385798100391. |
[7] |
S. Newhouse, Entropy and volume, Erg. Th. Dyn. Sys., 8 (1988), 283-299.
doi: 10.1017/S0143385700009469. |
[8] |
F. Przytycki, An upper estimation for topological entropy of diffeomorphisms, Inv. Math., 59 (1980), 205-213.
doi: 10.1007/BF01453234. |
[9] |
D. Ruelle, An inequality for the entropy of differentiable maps, Bol. Soc. Brasil. Mat., 9 (1978), 83-87.
doi: 10.1007/BF02584795. |
[10] |
R. Saghin, Note on homology of expanding foliations, Discr. Cont. Dyn. Sys.-Series S, 2 (2009), 349-360.
doi: 10.3934/dcdss.2009.2.349. |
[11] |
R. Saghin and Z. Xia, The entropy conjecture for partially hyperbolic diffeomorphisms with 1D center, Topol. and Appl., 157 (2010), 29-34.
doi: 10.1016/j.topol.2009.04.053. |
[12] |
Y. Yomdin, Volume growth and entropy, Israel J. Math., 57 (1987), 285-300.
doi: 10.1007/BF02766215. |
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] |
K. Burns and A. Wilkinson, On the ergodicity of partially hyperbolic systems, Ann. of Math. (2), 171 (2010), 451-489.
doi: 10.4007/annals.2010.171.451. |
[3] |
N. Gourmelon, Adapted metrics for dominated splittings, Erg. Th. Dyn. Syst., 27 (2007), 1839-1849.
doi: 10.1017/S0143385707000272. |
[4] |
Y. Hua, R. Saghin and Z. Xia, Topological entropy and partially hyperbolic diffeomorphisms, Erg. Th. Dynam. Syst., 28 (2008), 843-862.
doi: 10.1017/S0143385707000405. |
[5] |
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 Univ. Press, Cambridge, 1995. |
[6] |
O. Kozlovski, An integral formula for topological entropy of $C^{\infty}$ maps, Erg. Th. Dyn. Sys., 18 (1998), 405-424.
doi: 10.1017/S0143385798100391. |
[7] |
S. Newhouse, Entropy and volume, Erg. Th. Dyn. Sys., 8 (1988), 283-299.
doi: 10.1017/S0143385700009469. |
[8] |
F. Przytycki, An upper estimation for topological entropy of diffeomorphisms, Inv. Math., 59 (1980), 205-213.
doi: 10.1007/BF01453234. |
[9] |
D. Ruelle, An inequality for the entropy of differentiable maps, Bol. Soc. Brasil. Mat., 9 (1978), 83-87.
doi: 10.1007/BF02584795. |
[10] |
R. Saghin, Note on homology of expanding foliations, Discr. Cont. Dyn. Sys.-Series S, 2 (2009), 349-360.
doi: 10.3934/dcdss.2009.2.349. |
[11] |
R. Saghin and Z. Xia, The entropy conjecture for partially hyperbolic diffeomorphisms with 1D center, Topol. and Appl., 157 (2010), 29-34.
doi: 10.1016/j.topol.2009.04.053. |
[12] |
Y. Yomdin, Volume growth and entropy, Israel J. Math., 57 (1987), 285-300.
doi: 10.1007/BF02766215. |
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