scholarly journals Flexibility of Lyapunov exponents

2021 ◽  
pp. 1-38
Author(s):  
J. BOCHI ◽  
A. KATOK ◽  
F. RODRIGUEZ HERTZ
Keyword(s):  
Lyapunov Exponents ◽  
Anosov Diffeomorphisms ◽  
One Dimensional ◽  
Volume Preserving ◽  
Smooth Dynamics

Abstract We outline the flexibility program in smooth dynamics, focusing on flexibility of Lyapunov exponents for volume-preserving diffeomorphisms. We prove flexibility results for Anosov diffeomorphisms admitting dominated splittings into one-dimensional bundles.

On the integrability of intermediate distributions for Anosov diffeomorphisms

1995 ◽  
Vol 15 (2) ◽  
pp. 317-331 ◽  
Author(s):  
M. Jiang ◽  
Ya B. Pesin ◽  
R. de la Llave
Keyword(s):  
Finite Number ◽  
Lyapunov Exponents ◽  
Periodic Orbits ◽  
Three Dimensional ◽  
Dimensional Torus ◽  
Anosov Diffeomorphism ◽  
Anosov Diffeomorphisms ◽  
Stable Foliation

AbstractWe study the integrability of intermediate distributions for Anosov diffeomorphisms and provide an example of a C∞-Anosov diffeomorphism on a three-dimensional torus whose intermediate stable foliation has leaves that admit only a finite number of derivatives. We also show that this phenomenon is quite abundant. In dimension four or higher this can happen even if the Lyapunov exponents at periodic orbits are constant.

Poincaré Recurrences in a Nonautonomous Chaotic Map

2014 ◽  
Vol 24 (08) ◽  
pp. 1440016 ◽  
Author(s):  
Yaroslav Boev ◽  
Nadezhda Semenova ◽  
Galina Strelkova ◽  
Vadim Anishchenko
Keyword(s):  
Lyapunov Exponents ◽  
Distribution Density ◽  
Chaotic Map ◽  
Nonautonomous System ◽  
Harmonic Force ◽  
One Dimensional ◽  
The Relationship

The statistics of Poincaré recurrences is studied numerically in a one-dimensional cubic map in the presence of harmonic and noisy excitations. It is shown that the distribution density of Poincaré recurrences is periodically modulated by the harmonic force. It is established that the relationship between the Afraimovich–Pesin dimension and Lyapunov exponents is violated in the nonautonomous system.

scholarly journals Estimating invariant measures and Lyapunov exponents

1996 ◽  
Vol 16 (4) ◽  
pp. 735-749 ◽  
Author(s):  
Brian R. Hunt
Keyword(s):  
Invariant Measure ◽  
Lyapunov Exponents ◽  
Invariant Measures ◽  
Continuous Invariant Measure ◽  
Absolutely Continuous ◽  
One Dimensional ◽  
Recent Interest ◽  
Absolutely Continuous Invariant Measure ◽  
Time Averages ◽  
Absolutely Continuous Invariant

AbstractThis paper describes a method for obtaining rigorous numerical bounds on time averages for a class of one-dimensional expanding maps. The idea is to directly estimate the absolutely continuous invariant measure for these maps, without computing trajectories. The main theoretical result is a bound on the convergence rate of the Frobenius—Perron operator for such maps. The method is applied to estimate the Lyapunov exponents for a planar map of recent interest.

scholarly journals -openness of non-uniform hyperbolic diffeomorphisms with bounded -norm

2019 ◽  
Vol 40 (11) ◽  
pp. 3078-3104
Author(s):  
CHAO LIANG ◽  
KARINA MARIN ◽  
JIAGANG YANG
Keyword(s):  
Lyapunov Exponents ◽  
Dense Subset ◽  
Topological Properties ◽  
Hyperbolic Diffeomorphisms ◽  
Uniform Hyperbolicity ◽  
Partially Hyperbolic ◽  
The Stability ◽  
Bounded Norm ◽  
Volume Preserving

We study the $C^{1}$-topological properties of the subset of non-uniform hyperbolic diffeomorphisms in a certain class of $C^{2}$ partially hyperbolic symplectic systems which have bounded $C^{2}$ distance to the identity. In this set, we prove the stability of non-uniform hyperbolicity as a function of the diffeomorphism and the measure, and the existence of an open and dense subset of continuity points for the center Lyapunov exponents. These results are generalized to the volume-preserving context.

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