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Entropy-expansiveness for partially hyperbolic diffeomorphisms
1. | Dep. Matemática PUC-Rio, Marquês de São Vicente 225 22453-900, Rio de Janeiro, Brazil |
2. | Department of Mathematics, Brigham Young University, Provo, UT 84602 |
3. | Instituto de Matemática, Universidade Federal do Rio de Janeiro, P. O. Box 68530, 21945-970, Rio de Janeiro, Brazil |
4. | Instituto de Matematica, Regional Norte, Rivera 1350, Universidad de la Republica, CP 50000, Salto, Uruguay |
References:
[1] |
J. Alves, "Statistical Analysis Ofnon-uniformly Expanding Dynamical Systems," IMPA Mathematical Publications, 24, Colóquio Brasileiro de Matemática, (IMPA), 2003. |
[2] |
M. Asaoka, Hyperbolic sets exhibiting $C^1$-persistent homoclinic tangency for higher dimensions, Proc. Amer. Math. Soc., 136 (2008), 677-686.
doi: 10.1090/S0002-9939-07-09115-0. |
[3] |
C. Bonatti, L. J. Díaz and M. Viana, "Dynamics Beyond Uniform Hyperbolicity," Encyclopaedia of Mathematical Sciences, Math. Phys., 102, Springer-Verlag, Berlin, 2004. |
[4] |
R. Bowen, Entropy-expansive maps, Trans. A. M. S., 164 (1972), 323-331.
doi: 10.1090/S0002-9947-1972-0285689-X. |
[5] |
M. Boyle and T. Downarowicz, The entropy theory of symbolic extensions, Inventiones Math., 156 (2004), 119-161.
doi: 10.1007/s00222-003-0335-2. |
[6] |
M. Boyle, D. Fiebig and U. Fiebig, Residual entropy, conditional entropy, and subshift covers, Forum Math., 14 (2002), 713-757.
doi: 10.1515/form.2002.031. |
[7] |
D. Burguet, $C^2$ surface diffeomorphisms have symbolic extensions, preprint, arXiv:0912.2018. |
[8] |
K. Burns and A. Wilkinson, On the ergodicity of partially hyperbolic systems, Ann. of Math., 171 (2010), 451-489.
doi: 10.4007/annals.2010.171.451. |
[9] |
J. Buzzi, Intrinsic ergodicity for smooth interval maps, Israel J. Math., 100 (1997), 125-161.
doi: 10.1007/BF02773637. |
[10] |
J. Buzzi, T. Fisher, M. Sambarino and C. V\'asquez, Maximal entropy measures for certain partially hyperbolic, derived from Anosov systems, Ergod. Th. Dynamic. Systems, to appear. |
[11] |
W. Cowieson and L.-S. Young, SRB mesaures as zero-noise limits, Ergod. Th. Dynamic. Systems, 25 (2005), 1115-1138.
doi: 10.1017/S0143385704000604. |
[12] |
L. J. Díaz and T. Fisher, Symbolic extensions and partially hyperbolic diffeomorphisms, Discrete and Cont. Dynamic. Systems, 29 (2011), 1419-1441. |
[13] |
T. Downarowicz and A. Maass, Smooth interval maps have symbolic extensions, Inventiones Math., 176 (2009), 617-636.
doi: 10.1007/s00222-008-0172-4. |
[14] |
T. Downarowicz and S. Newhouse, Symbolic extensions and smooth dynamical systems, Inventiones Math., 160 (2005), 453-499.
doi: 10.1007/s00222-004-0413-0. |
[15] |
N. Gourmelon, Adapted metrics for dominated splittings, Ergod. Th. Dynamic. Systems, 27 (2007), 1839-1849. |
[16] |
M. W. Hirsch, C.C. Pugh and M.Shub, "Invariant Manifolds," Lecture Notes In Mathematics, 583, Springer-Verlag, Berlin-New York, 1977. |
[17] |
A. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems," Cambridge University Press, Cambridge, 1995. |
[18] |
G. Keller, "Equilibrium States in Ergodic Theory," London Mathematical Society Student Texts, Cambridge University Press, Cambridge, 1998. |
[19] |
G. Liao, M. Viana and J. Yang, The entropy conjecture for diffeomorphisms away from tangencies, preprint, arXiv:1012.0514. |
[20] |
M. Misiurewicz, Topological conditional entropy, Studia Math., 55 (1976), 175-200. |
[21] |
M. J. Pacifico and J. L. Vieitez, Entropyexpansiveness and domination for surface diffeomorphisms, Rev. Mat. Complut., 21 (2008), 293-317. |
[22] |
M. J. Pacifico and J. L. Vieitez, Robust entropy-expansiveness implies generic domination, Nonlinearity, 23 (2010), 1971-1990.
doi: 10.1088/0951-7715/23/8/009. |
[23] |
V. A. Pliss, Analysis of the necessity of the conditions of Smale and Robbinfor structural stability of periodic systems of differentialequations, Diff. Uravnenija, 8 (1972), 972-983. |
[24] |
R. Saghin and Z. Xia, The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center, Topology Appl., 157 (2010), 29-34. |
[25] |
M. Shub, Dynamical systems, filtrations and entropy, Bull. Amer. Math. Soc., 80 (1974), 27-41.
doi: 10.1090/S0002-9904-1974-13344-6. |
[26] |
L. Wen, Homoclinic tangencies and dominated splittings, Nonlinearity, 15 (2002), 1445-1469.
doi: 10.1088/0951-7715/15/5/306. |
show all references
References:
[1] |
J. Alves, "Statistical Analysis Ofnon-uniformly Expanding Dynamical Systems," IMPA Mathematical Publications, 24, Colóquio Brasileiro de Matemática, (IMPA), 2003. |
[2] |
M. Asaoka, Hyperbolic sets exhibiting $C^1$-persistent homoclinic tangency for higher dimensions, Proc. Amer. Math. Soc., 136 (2008), 677-686.
doi: 10.1090/S0002-9939-07-09115-0. |
[3] |
C. Bonatti, L. J. Díaz and M. Viana, "Dynamics Beyond Uniform Hyperbolicity," Encyclopaedia of Mathematical Sciences, Math. Phys., 102, Springer-Verlag, Berlin, 2004. |
[4] |
R. Bowen, Entropy-expansive maps, Trans. A. M. S., 164 (1972), 323-331.
doi: 10.1090/S0002-9947-1972-0285689-X. |
[5] |
M. Boyle and T. Downarowicz, The entropy theory of symbolic extensions, Inventiones Math., 156 (2004), 119-161.
doi: 10.1007/s00222-003-0335-2. |
[6] |
M. Boyle, D. Fiebig and U. Fiebig, Residual entropy, conditional entropy, and subshift covers, Forum Math., 14 (2002), 713-757.
doi: 10.1515/form.2002.031. |
[7] |
D. Burguet, $C^2$ surface diffeomorphisms have symbolic extensions, preprint, arXiv:0912.2018. |
[8] |
K. Burns and A. Wilkinson, On the ergodicity of partially hyperbolic systems, Ann. of Math., 171 (2010), 451-489.
doi: 10.4007/annals.2010.171.451. |
[9] |
J. Buzzi, Intrinsic ergodicity for smooth interval maps, Israel J. Math., 100 (1997), 125-161.
doi: 10.1007/BF02773637. |
[10] |
J. Buzzi, T. Fisher, M. Sambarino and C. V\'asquez, Maximal entropy measures for certain partially hyperbolic, derived from Anosov systems, Ergod. Th. Dynamic. Systems, to appear. |
[11] |
W. Cowieson and L.-S. Young, SRB mesaures as zero-noise limits, Ergod. Th. Dynamic. Systems, 25 (2005), 1115-1138.
doi: 10.1017/S0143385704000604. |
[12] |
L. J. Díaz and T. Fisher, Symbolic extensions and partially hyperbolic diffeomorphisms, Discrete and Cont. Dynamic. Systems, 29 (2011), 1419-1441. |
[13] |
T. Downarowicz and A. Maass, Smooth interval maps have symbolic extensions, Inventiones Math., 176 (2009), 617-636.
doi: 10.1007/s00222-008-0172-4. |
[14] |
T. Downarowicz and S. Newhouse, Symbolic extensions and smooth dynamical systems, Inventiones Math., 160 (2005), 453-499.
doi: 10.1007/s00222-004-0413-0. |
[15] |
N. Gourmelon, Adapted metrics for dominated splittings, Ergod. Th. Dynamic. Systems, 27 (2007), 1839-1849. |
[16] |
M. W. Hirsch, C.C. Pugh and M.Shub, "Invariant Manifolds," Lecture Notes In Mathematics, 583, Springer-Verlag, Berlin-New York, 1977. |
[17] |
A. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems," Cambridge University Press, Cambridge, 1995. |
[18] |
G. Keller, "Equilibrium States in Ergodic Theory," London Mathematical Society Student Texts, Cambridge University Press, Cambridge, 1998. |
[19] |
G. Liao, M. Viana and J. Yang, The entropy conjecture for diffeomorphisms away from tangencies, preprint, arXiv:1012.0514. |
[20] |
M. Misiurewicz, Topological conditional entropy, Studia Math., 55 (1976), 175-200. |
[21] |
M. J. Pacifico and J. L. Vieitez, Entropyexpansiveness and domination for surface diffeomorphisms, Rev. Mat. Complut., 21 (2008), 293-317. |
[22] |
M. J. Pacifico and J. L. Vieitez, Robust entropy-expansiveness implies generic domination, Nonlinearity, 23 (2010), 1971-1990.
doi: 10.1088/0951-7715/23/8/009. |
[23] |
V. A. Pliss, Analysis of the necessity of the conditions of Smale and Robbinfor structural stability of periodic systems of differentialequations, Diff. Uravnenija, 8 (1972), 972-983. |
[24] |
R. Saghin and Z. Xia, The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center, Topology Appl., 157 (2010), 29-34. |
[25] |
M. Shub, Dynamical systems, filtrations and entropy, Bull. Amer. Math. Soc., 80 (1974), 27-41.
doi: 10.1090/S0002-9904-1974-13344-6. |
[26] |
L. Wen, Homoclinic tangencies and dominated splittings, Nonlinearity, 15 (2002), 1445-1469.
doi: 10.1088/0951-7715/15/5/306. |
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