scholarly journals Bernoulli property for certain skew products over hyperbolic systems

2021 ◽  
pp. 1
Author(s):  
Changguang Dong ◽  
Adam Kanigowski
Keyword(s):  
Hyperbolic Systems ◽  
Skew Products

scholarly journals An analogue of Bauer’s theorem for closed orbits of skew products

2008 ◽  
Vol 28 (2) ◽  
pp. 535-546 ◽  
Author(s):  
WILLIAM PARRY ◽  
MARK POLLICOTT
Keyword(s):  
Number Theory ◽  
Algebraic Number ◽  
Hyperbolic Systems ◽  
Algebraic Number Theory ◽  
Skew Products ◽  
Closed Orbits

AbstractIn this article we prove an analogue of Bauer’s theorem from algebraic number theory in the context of hyperbolic systems.

scholarly journals Equilibrium stability for non-uniformly hyperbolic systems

2018 ◽  
Vol 39 (10) ◽  
pp. 2619-2642 ◽  
Author(s):  
JOSÉ F. ALVES ◽  
VANESSA RAMOS ◽  
JAQUELINE SIQUEIRA
Keyword(s):  
Hyperbolic Systems ◽  
Equilibrium States ◽  
Topological Pressure ◽  
Equilibrium Stability ◽  
Hölder Continuous ◽  
Skew Products ◽  
Uniformly Hyperbolic Systems ◽  
Wide Family

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 $\text{weak}^{\ast }$ topology within such systems.

Control of Pseudo-Hyperbolic Systems by Concentrated Impacts

2000 ◽  
Vol 32 (12) ◽  
pp. 23-36 ◽  
Author(s):  
Sergey I. Lyashko ◽  
Vladimir V. Semenov ◽  
Ivan I. Lyashko
Keyword(s):  
Hyperbolic Systems

scholarly journals Diffeomorphism cocycles over partially hyperbolic systems

2020 ◽  
pp. 1-24
Author(s):  
VICTORIA SADOVSKAYA
Keyword(s):  
Hyperbolic System ◽  
Compact Manifold ◽  
Hyperbolic Systems ◽  
Riemannian Metrics ◽  
Hölder Continuous ◽  
Group Of Diffeomorphisms ◽  
Small Loss ◽  
Partially Hyperbolic ◽  
Loss Of Regularity

Abstract We consider Hölder continuous cocycles over an accessible partially hyperbolic system with values in the group of diffeomorphisms of a compact manifold $\mathcal {M}$ . We obtain several results for this setting. If a cocycle is bounded in $C^{1+\gamma }$ , we show that it has a continuous invariant family of $\gamma $ -Hölder Riemannian metrics on $\mathcal {M}$ . We establish continuity of a measurable conjugacy between two cocycles assuming bunching or existence of holonomies for both and pre-compactness in $C^0$ for one of them. We give conditions for existence of a continuous conjugacy between two cocycles in terms of their cycle weights. We also study the relation between the conjugacy and holonomies of the cocycles. Our results give arbitrarily small loss of regularity of the conjugacy along the fiber compared to that of the holonomies and of the cocycle.

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