scholarly journals Stable ergodicity for partially hyperbolic attractors with positive central Lyapunov exponents

2009 ◽  
Vol 3 (2) ◽  
pp. 233-251 ◽  
Author(s):  
Carlos H. Vásquez ◽  
Keyword(s):  
Lyapunov Exponents ◽  
Stable Ergodicity ◽  
Hyperbolic Attractors ◽  
Partially Hyperbolic

scholarly journals Stable ergodicity for partially hyperbolic attractors with negative central exponents

2008 ◽  
Vol 2 (1) ◽  
pp. 63-81 ◽  
Author(s):  
Keith Burns ◽  
◽  
Dmitry Dolgopyat ◽  
Yakov Pesin ◽  
Mark Pollicott ◽  
...  
Keyword(s):  
Stable Ergodicity ◽  
Hyperbolic Attractors ◽  
Partially Hyperbolic

scholarly journals On the stable ergodicity of Berger–Carrasco’s example

2018 ◽  
Vol 40 (4) ◽  
pp. 1008-1056
Author(s):  
DAVI OBATA
Keyword(s):  
Lyapunov Exponents ◽  
Two Dimensional ◽  
Dominated Splitting ◽  
Standard Map ◽  
Hyperbolic Diffeomorphisms ◽  
Stable Ergodicity ◽  
Partially Hyperbolic ◽  
Partially Hyperbolic Diffeomorphism ◽  
Volume Preserving ◽  
Math Phys

We prove the stable ergodicity of an example of a volume-preserving, partially hyperbolic diffeomorphism introduced by Berger and Carrasco in [Berger and Carrasco. Non-uniformly hyperbolic diffeomorphisms derived from the standard map. Comm. Math. Phys.329 (2014), 239–262]. This example is robustly non-uniformly hyperbolic, with a two-dimensional center; almost every point has both positive and negative Lyapunov exponents along the center direction and does not admit a dominated splitting of the center direction. The main novelty of our proof is that we do not use accessibility.

scholarly journals SRB measures for partially hyperbolic attractors of local diffeomorphisms

2018 ◽  
Vol 40 (6) ◽  
pp. 1545-1593
Author(s):  
ANDERSON CRUZ ◽  
PAULO VARANDAS
Keyword(s):  
Thermodynamic Formalism ◽  
Positive Lebesgue Measure ◽  
Stable Bundle ◽  
Local Diffeomorphism ◽  
Local Diffeomorphisms ◽  
Axiom A ◽  
Srb Measures ◽  
Cone Field ◽  
Hyperbolic Attractors ◽  
Partially Hyperbolic

We contribute to the thermodynamic formalism of partially hyperbolic attractors for local diffeomorphisms admitting an invariant stable bundle and a positively invariant cone field with non-uniform cone expansion at a positive Lebesgue measure set of points. These include the case of attractors for Axiom A endomorphisms and partially hyperbolic endomorphisms derived from Anosov. We prove these attractors have finitely many SRB measures, that these are hyperbolic, and that the SRB measure is unique provided the dynamics is transitive. Moreover, we show that the SRB measures are statistically stable (in the weak$^{\ast }$ topology) and that their entropy varies continuously with respect to the local diffeomorphism.

scholarly journals Almost sure rates of mixing for partially hyperbolic attractors

2022 ◽  
Vol 311 ◽  
pp. 98-157
Author(s):  
José F. Alves ◽  
Wael Bahsoun ◽  
Marks Ruziboev
Keyword(s):  
Hyperbolic Attractors ◽  
Partially Hyperbolic

scholarly journals Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers

2004 ◽  
Vol 160 (2) ◽  
pp. 375-432 ◽  
Author(s):  
Carlos Morales Rojas ◽  
Maria Pacifico ◽  
Enrique Pujals
Keyword(s):  
Singular Sets ◽  
Hyperbolic Attractors ◽  
Partially Hyperbolic

scholarly journals Gibbs measures for partially hyperbolic attractors

1982 ◽  
Vol 2 (3-4) ◽  
pp. 417-438 ◽  
Author(s):  
Ya. B. Pesin ◽  
Ya. G. Sinai
Keyword(s):  
Special Form ◽  
Gibbs Measures ◽  
Hyperbolic Attractor ◽  
Absolutely Continuous ◽  
Unstable Manifolds ◽  
Hyperbolic Attractors ◽  
Partially Hyperbolic ◽  
Limit Points ◽  
Continuous Measures ◽  
Absolutely Continuous Measures

AbstractWe consider iterates of absolutely continuous measures concentrated in a neighbourhood of a partially hyperbolic attractor. It is shown that limit points can be measures which have conditional measures of a special form for any partition into subsets of unstable manifolds.

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