Statistical properties of the maximal entropy measure for partially hyperbolic attractors

Castro, Armando; Nascimento, Teófilo

doi:10.1017/etds.2015.86

Cited by 20 publications

(26 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Assume now that µ is an ergodic equilibrium state for (f, ϕ). Using (4), (10), (12), (13) and the fact that π * μ = µ, we obtain…”

Section: Skew Productsmentioning

confidence: 99%

“…Climenhaga, Fisher and Thompson in [14,15] address the question of existence and uniqueness of equilibrium states for Bonatti-Viana diffeomorphisms and Mañé diffeomorphisms for suitable classes of potentials. Castro and Nascimento in [12] showed uniqueness of the maximal entropy measure for partially hyperbolic attractors semiconjugated to nonuniformly expanding maps. For a family of partially hyperbolic horseshoes introduced by Díaz, Horita, Rios and Sambarino in [17] the existence of equilibrium states for any continuous potential was proved by Leplaideur, Oliveira and Rios in [19].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Equilibrium stability for non-uniformly hyperbolic systems

Alves¹,

Ramos²,

Siqueira³

2018

Ergod. Th. Dynam. Sys.

View full text Add to dashboard Cite

We prove that for a wide family of non-uniformly hyperbolic maps and hyperbolic potentials we have equilibrium stability, i.e. the equilibrium states depend continuously on the dynamics and the potential. For this we deduce that the topological pressure is continuous as a function of the dynamics and the potential. We also prove the existence of finitely many ergodic equilibrium states for non-uniformly hyperbolic skew products and hyperbolic Hölder continuous potentials. Finally we show that these equilibrium states vary continuously in the weak * topology within such systems.2010 Mathematics Subject Classification. 37A05, 37A35.

show abstract

“…Assume now that µ is an ergodic equilibrium state for (f, ϕ). Using (4), (10), (12), (13) and the fact that π * μ = µ, we obtain…”

Section: Skew Productsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Equilibrium stability for non-uniformly hyperbolic systems

Alves¹,

Ramos²,

Siqueira³

2018

Ergod. Th. Dynam. Sys.

View full text Add to dashboard Cite

show abstract

“…In particular, an example from [17,16] is given that illustrates the case where the pressure function is discontinuous and not strictly decreasing. An extension of the current results to the study of irregular sets for non-additive sequences of observables was carried out in [4], while we expect that these results can be also extended to the class of partially hyperbolic diffeomorphisms in [10].…”

Section: Introductionmentioning

confidence: 73%

Multifractal analysis for weak Gibbs measures: from large deviations to irregular sets

Bomfim¹,

Varandas²

2015

Ergod. Th. Dynam. Sys.

View full text Add to dashboard Cite

Abstract. In this article we prove estimates for the topological pressure of the set of points whose Birkhoff time averages are far from the space averages corresponding to the unique equilibrium state that has a weak Gibbs property. In particular, if f has an expanding repeller and φ is an Hölder continuous potential we prove that the topological pressure of the set of points whose accumulation values of Birkhoff averages belong to some interval I ⊂ R can be expressed in terms of the topological pressure of the whole system and the large deviations rate function. As a byproduct we deduce that most irregular sets for maps with the specification property have topological pressure strictly smaller than the whole system. Some extensions to a non-uniformly hyperbolic setting, level-2 irregular sets and hyperbolic flows are also given.

show abstract

“…Liverani in [28] used it to prove the exponential decay of correlations for smooth uniformly hyperbolic area-preserving cases. Later, it was generalized to general Axiom A attractors in [35,5], and some partially hyperbolic systems [2,12]. For RDS, the Birkhoff cone approach was used in [7] and [34] (we mentioned before) for exponential decay of (quenched) random correlations.…”

Section: Andmentioning

confidence: 99%