Lyapunov exponents and invariant manifolds for random dynamical systems in a Banach space

2010 ◽  
Vol 206 (967) ◽  
pp. 0-0 ◽  
Author(s):  
Zeng Lian ◽  
Kening Lu
Keyword(s):  
Banach Space ◽  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Invariant Manifolds ◽  
Random Dynamical Systems

Random entropy expansiveness for diffeomorphisms with dominated splittings

2019 ◽  
Vol 20 (02) ◽  
pp. 2050014
Author(s):  
Zeya Mi
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Random Dynamical Systems ◽  
Local Entropy ◽  
Dominated Splitting ◽  
One Dimensional ◽  
Hyperbolic Diffeomorphisms ◽  
Partially Hyperbolic ◽  
Bowen Balls ◽  
Partially Hyperbolic Diffeomorphisms

We study the local entropy of typical infinite Bowen balls in random dynamical systems, and show the random entropy expansiveness for [Formula: see text] partially hyperbolic diffeomorphisms with multi one-dimensional centers. Moreover, we consider [Formula: see text] diffeomorphism [Formula: see text] with dominated splitting [Formula: see text] such that [Formula: see text] for every [Formula: see text], and all the Lyapunov exponents are non-negative along [Formula: see text] and non-positive along [Formula: see text], we prove the asymptotically random entropy expansiveness for [Formula: see text].

A systematic study of heteroclinic cycles in dynamical systems with broken symmetries

1996 ◽  
Vol 126 (4) ◽  
pp. 885-909 ◽  
Author(s):  
Reiner Lauterbach ◽  
Stanislaus Maier-Paape ◽  
Ernst Reissner
Keyword(s):  
Banach Space ◽  
Dynamical Systems ◽  
Symmetry Breaking ◽  
Systematic Study ◽  
Invariant Manifolds ◽  
Sufficient Conditions ◽  
Compact Lie Group ◽  
Heteroclinic Cycles ◽  
Broken Symmetries ◽  
Necessary And Sufficient

Let X be a Banach space or a manifold and G a compact Lie group acting on X. We study G-equivariant (semi)flows on X in the context of forced symmetry breaking. After applying small symmetry breaking perturbations, certain generic invariant manifolds of the above flows persist slightly changed. We obtain necessary and sufficient conditions for the existence of heteroclinic cycles on the perturbed manifolds. Applications are given for the case G = SO(3).

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