scholarly journals Partially hyperbolic sets from a co-dimension one bifurcation

1995 ◽  
Vol 1 (2) ◽  
pp. 253-275 ◽  
Author(s):  
Todd Young ◽  
Keyword(s):  
Partially Hyperbolic ◽  
Dimension One ◽  
Hyperbolic Sets

scholarly journals The structure of the space of ergodic measures of transitive partially hyperbolic sets

2019 ◽  
Vol 190 (3) ◽  
pp. 441-479
Author(s):  
L. J. Díaz ◽  
K. Gelfert ◽  
T. Marcarini ◽  
M. Rams
Keyword(s):  
Ergodic Measures ◽  
Partially Hyperbolic ◽  
Hyperbolic Sets

Quasi-shadowing Property on Random Partially Hyperbolic Sets

2018 ◽  
Vol 34 (9) ◽  
pp. 1429-1444
Author(s):  
Lin Wang ◽  
Xin Sheng Wang ◽  
Yu Jun Zhu
Keyword(s):  
Shadowing Property ◽  
Partially Hyperbolic ◽  
Hyperbolic Sets

scholarly journals NON-HYPERBOLIC ERGODIC MEASURES AND HORSESHOES IN PARTIALLY HYPERBOLIC HOMOCLINIC CLASSES

2019 ◽  
Vol 19 (5) ◽  
pp. 1765-1792 ◽  
Author(s):  
Dawei Yang ◽  
Jinhua Zhang
Keyword(s):  
Topological Entropy ◽  
Classical Result ◽  
Ergodic Measure ◽  
Rich Family ◽  
Ergodic Measures ◽  
Partially Hyperbolic ◽  
Hyperbolic Sets ◽  
Homoclinic Classes

We study a rich family of robustly non-hyperbolic transitive diffeomorphisms and we show that each ergodic measure is approached by hyperbolic sets in weak$\ast$-topology and in entropy. For hyperbolic ergodic measures, it is a classical result of A. Katok. The novelty here is to deal with non-hyperbolic ergodic measures. As a consequence, we obtain the continuity of topological entropy.

scholarly journals CENTER MANIFOLDS FOR PARTIALLY HYPERBOLIC SETS WITHOUT STRONG UNSTABLE CONNECTIONS

2015 ◽  
Vol 15 (4) ◽  
pp. 785-828 ◽  
Author(s):  
Christian Bonatti ◽  
Sylvain Crovisier
Keyword(s):  
Center Manifolds ◽  
Compact Sets ◽  
Partially Hyperbolic ◽  
Hyperbolic Sets

We consider compact sets which are invariant and partially hyperbolic under the dynamics of a diffeomorphism of a manifold. We prove that such a set $K$ is contained in a locally invariant center submanifold if and only if each strong stable and strong unstable leaf intersects $K$ at exactly one point.

scholarly journals Partially hyperbolic sets with a dynamically minimal lamination

2018 ◽  
Vol 38 (6) ◽  
pp. 2717-2729
Author(s):  
Luiz Felipe Nobili França ◽  
Keyword(s):  
Partially Hyperbolic ◽  
Hyperbolic Sets

scholarly journals A link between topological entropy and Lyapunov exponents

2017 ◽  
Vol 39 (3) ◽  
pp. 620-637
Author(s):  
THIAGO CATALAN
Keyword(s):  
Lyapunov Exponents ◽  
Topological Entropy ◽  
Lower Semicontinuous ◽  
Periodic Points ◽  
Partial Hyperbolicity ◽  
Symplectic Diffeomorphisms ◽  
Symplectic Diffeomorphism ◽  
Partially Hyperbolic ◽  
Generic Set ◽  
Hyperbolic Sets

We show that a $C^{1}$-generic non-partially hyperbolic symplectic diffeomorphism $f$ has topological entropy equal to the supremum of the sum of the positive Lyapunov exponents of its hyperbolic periodic points. Moreover, we also prove that $f$ has topological entropy approximated by the topological entropy of $f$ restricted to basic hyperbolic sets. In particular, the topological entropy map is lower semicontinuous in a $C^{1}$-generic set of symplectic diffeomorphisms far from partial hyperbolicity.

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