Citation: |
[1] |
F. Abdenur, C. Bonatti, S. Crovisier, L. J. Díaz and G. Wen, Periodic points and homoclinic classes, Ergod. Th. Dynamic. Systems, 27 (2007), 1-22. |
[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 and L. J. Díaz, Persistent nonhyperbolic transitive diffeomorphisms, Ann. of Math., 143 (1996), 357-396.doi: 10.2307/2118647. |
[4] |
C. Bonatti and L. J. Díaz, Connexions hétéroclines et généricité d'une infinité de puits ou de sources, Ann. Scient. Éc. Norm. Sup., 32 (1999), 135-150. |
[5] |
C. Bonatti and S. Crovisier, Recurrence et généricité, Invent. Math., 158 (2004), 33-104. |
[6] |
C. Bonatti and L. J. Díaz, On maximal transitive sets of generic diffeomorphisms, Publ. Math. Inst. Hautes Études Sci., 96 (2002), 171-197. |
[7] |
C. Bonatti, L. J. Díaz and T. Fisher, Supergrowth of the number of periodic orbits for non-hyperbolic homoclinic classes, Discrete and Cont. Dynamic. Systems, 20 (2008), 589-604. |
[8] |
C. Bonatti, L. J. Díaz and E. Pujals, A $C^1$-generic dichotomy for diffeomorphisms; weak forms of hyperbolicity or infinitely many sinks or sources, Annals of Math., 158 (2003), 355-418.doi: 10.4007/annals.2003.158.355. |
[9] |
C. Bonatti, L. J. Díaz, and M. Viana, "Dynamics Beyond Uniform Hyperbolicity. A Global Geometric and Probabilistic Perspective," volume 102 of Encyclopaedia of Mathematical Sciences, Springer-Verlag, Berlin, 2005. |
[10] |
C. Bonatti and M. Viana, SRB measures for partially hyperbolic systems whose central direction is mostly contracting, Israel J. Math., 115 (2000), 157-193.doi: 10.1007/BF02810585. |
[11] |
Ch. Bonatti, L. J. Díaz, E.R. Pujals and J. Rocha, Robustly transitive sets and heterodimensional cycles, Astérisque, 286 (2003), 187-222. |
[12] |
M. Boyle and T. Downarowicz, Symbolic extension entropy: $C^r$ examples, products and flows, Discrete Contin. Dyn. Syst., 16 (2006), 329-341.doi: 10.3934/dcds.2006.16.329. |
[13] |
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. |
[14] |
M. Brin and Stuck G, "Introduction to Dynamical Systems," Cambridge University Press, 2002.doi: 10.1017/CBO9780511755316. |
[15] |
D. Burguet, $C^2$ surface diffeomorphisms have symbolic extensions, preprint, arXiv:0912.2018. |
[16] |
K. Burns, personal communication. |
[17] |
J. Buzzi, Intrinsic ergodicity for smooth interval maps, Isreal J. Math., 100 (1997), 125-161.doi: 10.1007/BF02773637. |
[18] |
J. Buzzi, T. Fisher, M. Sambarino and C. Vásquez, Intrinsic ergodicity for certain partially hyperbolic derived from Anosov systems, preprint. |
[19] |
A. Candel and L. Conlon, "Foliations I," volume 23 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 2000. |
[20] |
C. Carbalo, C. Morales and M. J. Pacifico, Homoclinic classes for generic $C^1$ vector fields, Ergod. Th. Dynamic. Systems, 23 (2003), 403-415. |
[21] |
W. Cowieson and L.-S. Young, SRB measures as zero-noise limits, Ergod. Th. Dynamic. Systems, 25 (2005), 1115-1138. |
[22] |
L. J. Díaz, E. Pujals and R. Ures, Partial hyperbolicity and robust transitivity, Acta Math., 183 (1999), 1-43.doi: 10.1007/BF02392945. |
[23] |
T. Downarowicz and A. Maass, Smooth interval maps have symbolic extensions, Inventiones Math., 176 (2009), 617-636.doi: 10.1007/s00222-008-0172-4. |
[24] |
T. Downarowicz and S. Newhouse, Symbolic extensions in smooth dynamical systems, Inventiones Math., 160 (2005), 453-499.doi: 10.1007/s00222-004-0413-0. |
[25] |
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. |
[26] |
S. Hayashi, Connecting invariant manifolds and the solution of the $C^1$ stability and $\omega$-stability conjectures for flows, Annals of Math., 145 (1997), 81-137.doi: 10.2307/2951824. |
[27] |
A. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems," Cambridge University Press, 1995. |
[28] |
G. Keller, "Equilibrium States in Ergodic Theory," London Mathematical Society Student Texts, Cambridge University Press, 1998. |
[29] |
R. Mañé, Contributions to the stability conjecture, Topology, 17 (1978), 383-396.doi: 10.1016/0040-9383(78)90005-8. |
[30] |
M. Misiurewicz, Diffeomorphim without any measure of maximal entropy, Bull. Acad. Pol. Sci., Ser Sci. Math, Astr. et Phys, 21 (1973), 903-910. |
[31] |
S. Newhouse, Hyperbolic limit sets, Trans. Amer. Math. Soc., 167 (1972), 125-150.doi: 10.1090/S0002-9947-1972-0295388-6. |
[32] |
S. Newhouse, Continuity properties of entropy, Annals of Math., 129 (1989), 215-235.doi: 10.2307/1971492. |
[33] |
M. J. Pacifico and J. Vieitez, Robust entropy-expansiveness implies generic domination, preprint, arXiv:0903.2948. |
[34] |
M. J. Pacifico and J. Vieitez, Entropy-expansiveness and domination for surface diffeomorphisms, Rev. Mat. Complut., 21 (2008), 293-317. |
[35] |
E. Pujals and M. Sambarino, Homoclinic tangencies and hyperbolicity for surface diffeomorphisms, Annals of Math., 151 (2000), 961-1023.doi: 10.2307/121127. |
[36] |
R. Saghin and Z. Xia, The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center, Topology Appl., 157 (2010), 29-34.doi: 10.1016/j.topol.2009.04.053. |
[37] |
M. Shub, Dynamical systems, filtrations and entropy, Bull. Amer. Math. Soc., 80 (1974), 27-41.doi: 10.1090/S0002-9904-1974-13344-6. |
[38] |
M. Shub, "Global Stability of Dynamical Systems," Springer-Verlag, New York, 1987. |
[39] |
K. Sigmund, Generic properties of invariant measures for Axiom-A-diffeomorphisms, Inventiones Math., 11 (1970), 99-109.doi: 10.1007/BF01404606. |
[40] |
C. P. Simon, Instability in Diff$(T^3)$ and the nongenericity of rational zeta function, Trans. Amer. Math. Soc., 174 (1972), 217-242. |
[41] |
P. Walters, "An Introduction to Ergodic Theory," volume 79 of Graduate Texts in Mathematics, Springer-Verlag, Berlin-New York, 1982. |