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216
Infinite dimensional SRB measures
, 1995
"... We review the basic steps leading to the construction of a SinaiRuelleBowen (SRB) measure for an infinite lattice of weakly coupled expanding circle maps, and we show that this measure has exponential decay of spacetime correlations. First, using the PerronFrobenius operator, one connects the dy ..."
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Cited by 8 (1 self)
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We review the basic steps leading to the construction of a SinaiRuelleBowen (SRB) measure for an infinite lattice of weakly coupled expanding circle maps, and we show that this measure has exponential decay of spacetime correlations. First, using the PerronFrobenius operator, one connects
Infinite dimensional SRB measures
, 1995
"... We review the basic steps leading to the construction of a SinaiRuelleBowen (SRB) measure for an infinite lattice of weakly coupled expanding circle maps, and we show that this measure has exponential decay of spacetime correlations. First, using the PerronFrobenius operator, one connects the dy ..."
Abstract
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We review the basic steps leading to the construction of a SinaiRuelleBowen (SRB) measure for an infinite lattice of weakly coupled expanding circle maps, and we show that this measure has exponential decay of spacetime correlations. First, using the PerronFrobenius operator, one connects
SRB MEASURES FOR HYPERBOLIC POLYGONAL BILLIARDS
, 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
"... Abstract. Let Λ be a basic set of an Axiom A endomorphism on ndimensional compact Riemannian manifold. In this paper, we provide equivalent conditions for the existence of a SRB measure on Λ. In particular, we show that under the assumption that the closure of the postcritical set of f is disjoin ..."
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Abstract. Let Λ be a basic set of an Axiom A endomorphism on ndimensional compact Riemannian manifold. In this paper, we provide equivalent conditions for the existence of a SRB measure on Λ. In particular, we show that under the assumption that the closure of the postcritical set of f
SRB MEASURES FOR WEAKLY EXPANDING MAPS
, 2006
"... Abstract. We construct SRB measures for endomorphisms satisfying conditions far weaker than the usual nonuniform expansion. As a consequence, the definition of a nonuniformly expanding map can be weakened. We also prove the existence of an absolutely continuous invariant measure for local diffeomo ..."
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Cited by 8 (2 self)
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Abstract. We construct SRB measures for endomorphisms satisfying conditions far weaker than the usual nonuniform expansion. As a consequence, the definition of a nonuniformly expanding map can be weakened. We also prove the existence of an absolutely continuous invariant measure for local
SRB MEASURES FOR CERTAIN MARKOV PROCESSES
, 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 (SinaiRuelleBowen) 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 (SinaiRuelleBowen) measures for the IFS
SRB measures as zeronoise limits
, 2004
"... We consider zeronoise 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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Cited by 8 (0 self)
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We consider zeronoise 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
"... 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
, 2000
"... We construct SinaiRuelleBowen (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 nonuniformly expanding. If the r ..."
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Cited by 197 (44 self)
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We construct SinaiRuelleBowen (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 nonuniformly expanding
Multicomponent dynamical systems: SRB measures and phase transitions
, 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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Cited by 11 (2 self)
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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
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216