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http://dx.doi.org/10.11568/kjm.2018.26.2.327

SRB MEASURES IN CHAOTIC DYNAMICAL SYSTEMS  

Lee, Hyundeok (Department of Mathematics Education Cheongju University)
Publication Information
Korean Journal of Mathematics / v.26, no.2, 2018 , pp. 327-335 More about this Journal
Abstract
In this paper, we present the construction of natural invariant measures so called SRB(Sinai-Ruelle-Bowen) measures by the properties of geometric t-potential and Bowen's equation for the hyperbolic attractors.
Keywords
SRB measures; Lyapunov exponents; Pesin's entropy formula; Non-uniformly hyperbolic dynamical systems;
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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.   DOI
2 R. Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Lecture Notes in Mathematics 470, Springer-Verlag, 1975.
3 R. Bowen and D. Ruelle, The ergodic theory of axiom A flows, Inv. Math. 29(1975), 181-202.   DOI
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.   DOI
5 M. Hirsch, C. Pugh, and M. Shub, Invariant Manifolds, Lecture Notes in Mathematics 583, Springer-Verlag, 1977.
6 A. Katok, Lyapunov exponents, entropy and periodic orbits for diffeomorphisms, Publications de l'IHES 51 (1980), 137-174.   DOI
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.
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.   DOI
9 V. I. Oseledec, Multiplicative ergodic theorem, Lyapunov numbers for dynamical systems, Trans. Moscow Math. Soc. 19 (1968), 197-221.
10 Ya. Pesin, Characteristic Lyapunov exponents and smooth ergodic theory, Russian Math. Surveys 32 (4) (1977), 55-114.   DOI
11 Ya. Pesin, Dynamical systems with generalized hyperbolic attractors : hyperbolic, ergodic and topological properties, Ergodic Theory Dyn. Syst. 12 (1) (1992), 123-151.
12 D. Ruelle, A measure associated with axiom-A attractors, Am. J. Math. 98 (3) (1976), 619-654.   DOI
13 S. Smale, Differentiable dynamical systems, Bull. Am. Math. Soc. 73 (1967), 747-817. response, Nonlinear Anal. 57 (2004) 421-433.   DOI
14 Ya. Sinai, Gibbs measures in ergodic theory, Uspehi Mat. Nauk 27 (4) (1972), 21-64.
15 Lai-Sang Young, Statistical properties of dynamical systems with some hyperbolicity, Ann. Math. 2 147 (3) (1998), 585-650.   DOI
16 Lai-Sang Young, What are SRB measures, and which dynamical systems have them?, J. Stat. Phys 108 (2002), 733-754.   DOI