# SRB measures in chaotic dynamical systems

## Main Article Content

## Abstract

## Article Details

## Supporting Agencies

## References

[1] A. Avila and J. Bochi, Nonuniform hyperbolicity, global dominated splittings and generic properties of volume-preserving diffeomorphisms, Trans. Am. Math. Soc. 364 (6) (2012), 2883–2907. Google Scholar

[2] R. Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Lecture Notes in Mathematics 470, Springer-Verlag, 1975. Google Scholar

[3] R. Bowen and D. Ruelle, The ergodic theory of axiom A flows, Inv. Math. 29(1975), 181–202. Google Scholar

[4] V. Climenhaga, D. Dolgopyat, and Ya. Pesin, Non-stationary non-uniformly hyperbolicity : SRB measures for non-uniformly hyperbolic attractors, Commun. Math. Phys. 346 (2)(2016), 553–602. Google Scholar

[5] M. Hirsch, C. Pugh, and M. Shub, Invariant Manifolds, Lecture Notes in Mathematics 583, Springer-Verlag, 1977. Google Scholar

[6] A. Katok, Lyapunov exponents, entropy and periodic orbits for diffeomorphisms, Publications de l’IHES 51 (1980), 137–174. Google Scholar

[7] F. Ledrappier and J. M. Strelcyn, A proof of estimation from below in Pesin’s entropy formula, Ergodic Theory Dyn. Syst. (2) (1982), 203–219. Google Scholar

[8] F. Ledrappier and L. -S. Young, The metric entropy of diffeomorphisms, 1, Characterization of measures satisfying Pesin’s entropy formula, Ann. Math. 2. 122 (3) (1985), 509–539. Google Scholar

[9] V. I. Oseledec, Multiplicative ergodic theorem, Lyapunov numbers for dynamical systems, Trans. Moscow Math. Soc. 19 (1968), 197–221. Google Scholar

[10] Ya. Pesin, Characteristic Lyapunov exponents and smooth ergodic theory, Russian Math. Surveys 32 (4) (1977), 55–114. Google Scholar

[11] Ya. Pesin, Dynamical systems with generalized hyperbolic attractors : hyperbolic, ergodic and topological properties, Ergodic Theory Dyn. Syst. 12 (1) (1992), 123– 151. Google Scholar

[12] D. Ruelle, A measure associated with axiom-A attractors, Am. J. Math. 98 (3) (1976), 619–654. Google Scholar

[13] S. Smale, Differentiable dynamical systems, Bull. Am. Math. Soc. 73 (1967), 747–817. response, Nonlinear Anal. 57 (2004) 421–433. Google Scholar

[14] Ya. Sinai, Gibbs measures in ergodic theory, Uspehi Mat. Nauk 27 (4) (1972), 21–64. Google Scholar

[15] Lai-Sang Young, Statistical properties of dynamical systems with some hyperbolicity, Ann. Math. 2 147 (3) (1998), 585–650. Google Scholar

[16] Lai-Sang Young, What are SRB measures, and which dynamical systems have them?, J. Stat. Phys 108 (2002), 733–754. Google Scholar