On Pesin's entropy formula for dominated splittings without mixed behavior

Journal of Differential Equations - Tập 261 - Trang 3964-3986 - 2016
Yongluo Cao1, Dawei Yang1
1School of Mathematical Sciences, Soochow University, Suzhou 215006, PR China

Tài liệu tham khảo

Bowen, 1972, Entropy-expansive maps, Trans. Amer. Math. Soc., 164, 323, 10.1090/S0002-9947-1972-0285689-X Bowen, 1975, The ergodic theory of Axiom A flows, Invent. Math., 29, 181, 10.1007/BF01389848 Boyle, 2002, Residual entropy, conditional entropy and subshift covers, Forum Math., 14, 713, 10.1515/form.2002.031 Campbell, 2001, A generic C1 expanding map has a singular S-R-B measure, Comm. Math. Phys., 221, 335, 10.1007/s002200100491 Cao, 2003, Non-zero Lyapunov exponents and uniform hyperbolicity, Nonlinearity, 16, 1473, 10.1088/0951-7715/16/4/316 Catsigeras, 2015, The Pesin entropy formula for diffeomorphisms with dominated splitting, Ergodic Theory Dynam. Systems, 35, 737, 10.1017/etds.2013.93 Cowieson, 2005, SRB measures as zero-noise limits, Ergodic Theory Dynam. Systems, 25, 1115, 10.1017/S0143385704000604 Hirsch, 1977, Invariant Manifolds, vol. 583 R. Leplaideur, D. Yang, On the existence of SRB measures for singular hyperbolic attractors, 2015, in preparation. Liu, 2015, A note on partially hyperbolic attractors: entropy conjecture and SRB measures, Discrete Contin. Dyn. Syst., 35, 341, 10.3934/dcds.2015.35.341 Liao, 2013, Then entropy conjecture for diffeomorphisms away from tangencies, J. Eur. Math. Soc. (JEMS), 15, 2043, 10.4171/JEMS/413 Manning, 1975, Topological entropy and the first homology group, vol. 468, 185 Pliss, 1972, A hypothesis due to Smale, Differ. Equ., 8, 203 Qiu, 2011, Existence and uniqueness of SRB measure on C1 generic hyperbolic attractors, Comm. Math. Phys., 302, 345, 10.1007/s00220-010-1160-2 Ruelle, 1975, Currents, flows and diffeomorphisms, Topology, 14, 319, 10.1016/0040-9383(75)90016-6 Saghin, 2010, The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center, Topology Appl., 157, 29, 10.1016/j.topol.2009.04.053 Shub, 1974, Dynamical systems, filtrations and entropy, Bull. Amer. Math. Soc., 80, 27, 10.1090/S0002-9904-1974-13344-6 Shub, 1975, Entropy and stability, Topology, 14, 329, 10.1016/0040-9383(75)90017-8 Sun, 2012, Dominated splitting and Pesin's entropy formula, Discrete Contin. Dyn. Syst., 32, 1421, 10.3934/dcds.2012.32.1421 Tahzibi, 2002, C1-generic Pesin's entropy formula, C. R. Math. Acad. Sci. Paris, Ser. I, 335, 1057, 10.1016/S1631-073X(02)02609-2 Walters, 1982, An Introduction to Ergodic Theory, vol. 79 Yomdin, 1987, Volume growth and entropy, Israel J. Math., 57, 285, 10.1007/BF02766215