Lyapunov exponents

The dissertation is divided into four chapters: Chapter 1 - Preliminaries; Chapter 2 - Lyapunov exponents for dynamic equations; Chapter 3 - Bohl exponents for implicit dynamic equations; Chapter 4 - Stability radius for implicit dynamic equations.

117p monsterhunterer 20-06-2021 19 2   Download

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.

39p dontetvui 17-01-2013 41 7   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:

64p noel_noel 17-01-2013 33 5   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. ...

59p tuanloccuoi 04-01-2013 55 8   Download