Lyapunov exponents

Xem 1-4 trên 4 kết quả Lyapunov exponents
  • We prove that for any s 0 the majority of C s linear cocycles over any hyperbolic (uniformly or not) ergodic transformation exhibit some nonzero Lyapunov exponent: this is true for an open dense subset of cocycles and, actually, vanishing Lyapunov exponents correspond to codimension-∞. This open dense subset is described in terms of a geometric condition involving the behavior of the cocycle over certain heteroclinic orbits of the transformation.

    pdf39p dontetvui 17-01-2013 20 5   Download

  • We show that the integrated Lyapunov exponents of C 1 volume-preserving diffeomorphisms are simultaneously continuous at a given diffeomorphism only if the corresponding Oseledets splitting is trivial (all Lyapunov exponents are equal to zero) or else dominated (uniform hyperbolicity in the projective bundle) almost everywhere. We deduce a sharp dichotomy for generic volume-preserving diffeomorphisms on any compact manifold:

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  • In this paper we consider the upper (lower) - stability of Lyapunov exponents of linear differential equations in Rn . Sufficient conditions for the upper - stability of maximal exponent of linear systems under linear perturbations are given. The obtained results are extended to the system with nonlinear perturbations.

    pdf8p tuanlocmuido 19-12-2012 16 2   Download

  • Inspired by Lorenz’ remarkable chaotic flow, we describe in this paper the structure of all C 1 robust transitive sets with singularities for flows on closed 3-manifolds: they are partially hyperbolic with volume-expanding central direction, and are either attractors or repellers. In particular, any C 1 robust attractor with singularities for flows on closed 3-manifolds always has an invariant foliation whose leaves are forward contracted by the flow, and has positive Lyapunov exponent at every orbit, showing that any C 1 robust attractor resembles a geometric Lorenz attractor. ...

    pdf59p tuanloccuoi 04-01-2013 28 6   Download

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