scholarly journals SRB measures for some diffeomorphisms with dominated splittings as zero noise limits

2019 ◽  
Vol 39 (11) ◽  
pp. 6441-6465
Author(s):  
Zeya Mi ◽  
Keyword(s):  
Srb Measures

scholarly journals The set of points with Markovian symbolic dynamics for non-uniformly hyperbolic diffeomorphisms

2020 ◽  
pp. 1-26
Author(s):  
SNIR BEN OVADIA
Keyword(s):  
Symbolic Dynamics ◽  
Full Measure ◽  
Probability Measures ◽  
Positive Entropy ◽  
Surface Diffeomorphisms ◽  
Srb Measures ◽  
Hyperbolic Diffeomorphisms ◽  
Set Of Points ◽  
Math Phys ◽  
Homoclinic Classes

Abstract The papers [O. M. Sarig. Symbolic dynamics for surface diffeomorphisms with positive entropy. J. Amer. Math. Soc.26(2) (2013), 341–426] and [S. Ben Ovadia. Symbolic dynamics for non-uniformly hyperbolic diffeomorphisms of compact smooth manifolds. J. Mod. Dyn.13 (2018), 43–113] constructed symbolic dynamics for the restriction of $C^r$ diffeomorphisms to a set $M'$ with full measure for all sufficiently hyperbolic ergodic invariant probability measures, but the set $M'$ was not identified there. We improve the construction in a way that enables $M'$ to be identified explicitly. One application is the coding of infinite conservative measures on the homoclinic classes of Rodriguez-Hertz et al. [Uniqueness of SRB measures for transitive diffeomorphisms on surfaces. Comm. Math. Phys.306(1) (2011), 35–49].

An analytical construction of the SRB measures for Baker-type maps

1998 ◽  
Vol 8 (2) ◽  
pp. 424-443 ◽  
Author(s):  
S. Tasaki ◽  
Thomas Gilbert ◽  
J. R. Dorfman
Keyword(s):  
Srb Measures ◽  
Analytical Construction

SRB measures for attractors with continuous invariant splittings

2017 ◽  
Vol 288 (1-2) ◽  
pp. 135-165 ◽  
Author(s):  
Zeya Mi ◽  
Yongluo Cao ◽  
Dawei Yang
Keyword(s):  
Srb Measures

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.

Hyperbolic SRB Measures and the Leaf Condition

2021 ◽  
Vol 387 (3) ◽  
pp. 1353-1404 ◽  
Author(s):  
Snir Ben Ovadia
Keyword(s):  
Srb Measures

Sinai’s Work on Markov Partitions and SRB Measures

2019 ◽  
pp. 257-285 ◽  
Author(s):  
Yakov Pesin
Keyword(s):  
Markov Partitions ◽  
Srb Measures

scholarly journals Equivalence of physical and SRB measures in random dynamical systems

Nonlinearity ◽  
2019 ◽  
Vol 32 (4) ◽  
pp. 1494-1524 ◽  
Author(s):  
Alex Blumenthal ◽  
Lai-Sang Young
Keyword(s):  
Dynamical Systems ◽  
Random Dynamical Systems ◽  
Srb Measures

scholarly journals Singular SRB Measures for a Non 1–1 Map of the Unit Square

2016 ◽  
Vol 165 (2) ◽  
pp. 409-433 ◽  
Author(s):  
Paweł Góra ◽  
Abraham Boyarsky ◽  
Zhenyang Li
Keyword(s):  
Unit Square ◽  
Srb Measures

SRB measures for pointwise hyperbolic systems on open regions

2020 ◽  
Vol 63 (9) ◽  
pp. 1671-1720
Author(s):  
Jianyu Chen ◽  
Huyi Hu ◽  
Yunhua Zhou
Keyword(s):  
Hyperbolic Systems ◽  
Srb Measures
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