Citation: |
[1] |
F. Abdenur and M. Viana, Flavors of partial hyperbolicity, preprint, 2008. |
[2] |
J. Alves and V. Pinheiro, Topological structure of (partially) hyperbolic sets with positive volume, Trans. Amer. Math. Soc., 360 (2008), 5551-5569.doi: 10.1090/S0002-9947-08-04484-X. |
[3] |
A. Avila and J. Bochi, A generic $C^1$ map has no absolutely continuous invariant probability measure, Nonlinearity, 19 (2006), 2717-2725.doi: 10.1088/0951-7715/19/11/011. |
[4] |
J. Bochi and M. Viana, Lyapunov exponents: How frequently are dynamical systems hyperbolic?, in "Modern Dynamical Systems and Applications," Cambridge Univ. Press, Cambridge, (2004), 271-297. |
[5] |
R. Bowen, A horseshoe with positive measure, Invent. Math., 29 (1975), 203-204.doi: 10.1007/BF01389849. |
[6] |
R. Bowen, "Equilibrium States and the Ergodic Theory of Axiom A Diffeomorphisms," Lecture Notes in Mathematics, 470, Springer-Verlag, Berlin-New York, 1975. |
[7] |
M. Brin, Topological transitivity of a certain class of dynamical systems, and flows of frames on manifolds of negative curvature, Functional Anal. Appl., 9 (1975), 8-16.doi: 10.1007/BF01078168. |
[8] |
J. Pesin and M. Brin, Partially hyperbolic dynamical systems, (Russian), Izv. Akad. Nauk SSSR Ser. Mat., 38 (1974), 170-212. |
[9] |
M. Brin and G. Stuck, "Introduction to Dynamical Systems," Cambridge University Press, Cambridge, 2002.doi: 10.1017/CBO9780511755316. |
[10] |
K. Burns and A. Wilkinson, On the ergodicity of partially hyperbolic systems, Annals of Math. (2), 171 (2010), 451-489. |
[11] |
K. Burns, D. Dolgopyat and Ya. Pesin, Partial hyperbolicity, Lyapunov exponents and stable ergodicity, J. Statist. Phys., 108 (2002), 927-942.doi: 10.1023/A:1019779128351. |
[12] |
D. Dolgopyat and A Wilkinson, Stable accessibility is $C^1$ dense, in "Geometric Methods in Dynamics (II)", Astérisque 287 (2003), 33-60. |
[13] |
T. Fisher, "On the Structure of Hyperbolic Sets," Ph.D thesis, Northwestern University, 2004. |
[14] |
J. Franks, Necessary conditions for stability of diffeomorphisms, Trans. Amer. Math. Soc., 158 (1971), 301-308.doi: 10.1090/S0002-9947-1971-0283812-3. |
[15] |
H. Furstenberg, "Recurrence in Ergodic Theory and Combinatorial Number Theory," M. B. Porter Lectures, Princeton University Press, Princeton, N.J., 1981. |
[16] |
N. Gourmelon, Adapted metrics for dominated splittings, Ergod. Th. Dynam. Sys., 27 (2007), 1839-1849.doi: 10.1017/S0143385707000272. |
[17] |
M. Hirsch, C. Pugh and M. Shub, "Invariant Manifolds," Lecture Notes in Mathematics, 583, Springer-Verlag, Berlin-New York, 1977. |
[18] |
V. Niţică and A. Török, An open dense set of stably ergodic diffeomorphisms in a neighborhood of a non-ergodic one, Topology, 40 (2001), 259-278.doi: 10.1016/S0040-9383(99)00060-9. |
[19] |
C. Pugh and M. Shub, Stable ergodicity and julienne quasi-conformality, J. Eur. Math. Soc., 2 (2000), 1-52.doi: 10.1007/s100970050013. |
[20] |
C. Robinson and L. S. Young, Nonabsolutely continuous foliations for an Anosov diffeomorphism, Invent. Math., 61 (1980), 159-176.doi: 10.1007/BF01390119. |
[21] |
F. Rodriguez Hertz, M. Rodriguez Hertz and R. Ures, A survey of partially hyperbolic dynamics, in "Partially Hyperbolic Dynamics, Laminations, and Teichmüller Flow," 35-87, Fields Inst. Commun., 51, Amer. Math. Soc., 2007. |
[22] |
A. Wilkinson, The cohomological equation for partially hyperbolic diffeomorphisms, arXiv:0809.4862. |
[23] |
Z. Xia, Hyperbolic invariant sets with positive measures, Discrete Contin. Dyn. Syst., 15 (2006), 811-818.doi: 10.3934/dcds.2006.15.811. |