Results 1 - 10 of 216

Infinite dimensional SRB measures

by J. Bricmont , A. Kupiainen , 1995
"... We review the basic steps leading to the construction of a Sinai-Ruelle-Bowen (SRB) measure for an infinite lattice of weakly coupled expanding circle maps, and we show that this measure has exponential decay of space-time correlations. First, using the Perron-Frobenius operator, one connects the dy ..."
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We review the basic steps leading to the construction of a Sinai-Ruelle-Bowen (SRB) measure for an infinite lattice of weakly coupled expanding circle maps, and we show that this measure has exponential decay of space-time correlations. First, using the Perron-Frobenius operator, one connects

Infinite dimensional SRB measures

by unknown authors , 1995
"... We review the basic steps leading to the construction of a Sinai-Ruelle-Bowen (SRB) measure for an infinite lattice of weakly coupled expanding circle maps, and we show that this measure has exponential decay of space-time correlations. First, using the Perron-Frobenius operator, one connects the dy ..."
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We review the basic steps leading to the construction of a Sinai-Ruelle-Bowen (SRB) measure for an infinite lattice of weakly coupled expanding circle maps, and we show that this measure has exponential decay of space-time correlations. First, using the Perron-Frobenius operator, one connects

SRB MEASURES FOR HYPERBOLIC POLYGONAL BILLIARDS

by Gianluigi Del Magno, João Lopes Dias, Pedro Duarte, José Pedro Gaivão, Diogo Pinheiro , 2013
"... We prove that polygonal billiards with contracting reflection laws exhibit hyperbolic attractors with countably many ergodic SRB measures. These measures are robust under small perturbations of the reflection law, and the tables for which they exist form a generic set in the space of all polygons. ..."
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We prove that polygonal billiards with contracting reflection laws exhibit hyperbolic attractors with countably many ergodic SRB measures. These measures are robust under small perturbations of the reflection law, and the tables for which they exist form a generic set in the space of all polygons

SRB MEASURES FOR AXIOM A ENDOMORPHISMS

by Mariusz Urbanski, Christian Wolf
"... Abstract. Let Λ be a basic set of an Axiom A endomorphism on n-dimensional compact Riemannian manifold. In this paper, we provide equivalent conditions for the existence of a SRB measure on Λ. In par-ticular, we show that under the assumption that the closure of the post-critical set of f is disjoin ..."
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Abstract. Let Λ be a basic set of an Axiom A endomorphism on n-dimensional compact Riemannian manifold. In this paper, we provide equivalent conditions for the existence of a SRB measure on Λ. In par-ticular, we show that under the assumption that the closure of the post-critical set of f

SRB MEASURES FOR WEAKLY EXPANDING MAPS

by Vilton Pinheiro , 2006
"... Abstract. We construct SRB measures for endomorphisms satisfying conditions far weaker than the usual non-uniform expansion. As a consequence, the definition of a non-uniformly expanding map can be weakened. We also prove the existence of an absolutely continuous invariant measure for local diffeomo ..."
Abstract - Cited by 8 (2 self) - Add to MetaCart
Abstract. We construct SRB measures for endomorphisms satisfying conditions far weaker than the usual non-uniform expansion. As a consequence, the definition of a non-uniformly expanding map can be weakened. We also prove the existence of an absolutely continuous invariant measure for local

SRB MEASURES FOR CERTAIN MARKOV PROCESSES

by Wael Bahsoun, G Óra , 907
"... Abstract. We study Markov processes generated by iterated function systems (IFS). The constituent maps of the IFS are monotonic transformations of the interval with common fixed points at 0 and 1. We first obtain an upper bound on the number of SRB (Sinai-Ruelle-Bowen) measures for the IFS. Then the ..."
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Abstract. We study Markov processes generated by iterated function systems (IFS). The constituent maps of the IFS are monotonic transformations of the interval with common fixed points at 0 and 1. We first obtain an upper bound on the number of SRB (Sinai-Ruelle-Bowen) measures for the IFS

SRB measures as zero-noise limits

by William Cowieson, Lai-sang Young , 2004
"... We consider zero-noise limits of random perturbations of dynamical systems and examine, in terms of the continuity of entropy and Lyapunov exponents, circumstances under which these limits are SRB measures. The ideas of this general discussion are then applied to specific classes of attractors. We p ..."
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We consider zero-noise limits of random perturbations of dynamical systems and examine, in terms of the continuity of entropy and Lyapunov exponents, circumstances under which these limits are SRB measures. The ideas of this general discussion are then applied to specific classes of attractors. We

UNIQUENESS OF SRB MEASURES FOR TRANSITIVE DIFFEOMORPHISMS ON SURFACES

by F. Rodriguez Hertz, M. A. Rodriguez Hertz, A. Tahzibi, R. Ures
"... Abstract. We give a description of ergodic components of SRB measures in terms of ergodic homoclinic classes associated to hyperbolic periodic points. For transitive surface diffeomorphisms, we prove that there exists at most one SRB measure. 1. ..."
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Abstract. We give a description of ergodic components of SRB measures in terms of ergodic homoclinic classes associated to hyperbolic periodic points. For transitive surface diffeomorphisms, we prove that there exists at most one SRB measure. 1.

SRB measures for partially hyperbolic systems whose central direction is mostly expanding

by José F. Alves, Christian Bonatti, Marcelo Viana , 2000
"... We construct Sinai-Ruelle-Bowen (SRB) measures supported on partially hyperbolic sets of diffeomorphisms -- the tangent bundle splits into two invariant subbundles, one of which is uniformly contracting -- under the assumption that the complementary subbundle is non-uniformly expanding. If the r ..."
Abstract - Cited by 197 (44 self) - Add to MetaCart
We construct Sinai-Ruelle-Bowen (SRB) measures supported on partially hyperbolic sets of diffeomorphisms -- the tangent bundle splits into two invariant subbundles, one of which is uniformly contracting -- under the assumption that the complementary subbundle is non-uniformly expanding

Multicomponent dynamical systems: SRB measures and phase transitions

by Michael Blank, Leonid Bunimovich , 2002
"... We discuss a notion of phase transitions in multicomponent systems and clarify relations between deterministic chaotic and stochastic models of this type of systems. Connections between various de nitions of SRB measures are considered as well. ..."
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We discuss a notion of phase transitions in multicomponent systems and clarify relations between deterministic chaotic and stochastic models of this type of systems. Connections between various de nitions of SRB measures are considered as well.
Results 1 - 10 of 216