Hyperbolic systems

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 44 8   Download

Annals of Mathematics In this paper we will solve one of the central problems in dynamical systems: Theorem 1 (Density of hyperbolicity for real polynomials). Any real polynomial can be approximated by hyperbolic real polynomials of the same degree. Here we say that a real polynomial is hyperbolic or Axiom A, if the real line is the union of a repelling hyperbolic set, the basin of hyperbolic attracting periodic points and the basin of infinity.

39p noel_noel 17-01-2013 51 5   Download

Exponential decay of correlations for C 4 contact Anosov flows is established. This implies, in particular, exponential decay of correlations for all smooth geodesic flows in strictly negative curvature. 1. Introduction The study of decay of correlations for hyperbolic systems goes back to the work of Sinai [36] and Ruelle [32]. While many results were obtained through the years for maps, some positive results have been established for Anosov flows only recently. Notwithstanding the proof of ergodicity, and mixing, for geodesic flows on manifolds of negative curvature [15], [1], [35], ...

39p tuanloccuoi 04-01-2013 65 8   Download

Trong bài báo này, chúng ta nghiên cứu hyperbolicity của một số hệ thống bình thường của firstorder phi tuyến tính phương trình vi phân từng phần, mà một số MongeAmp đa chiều `lại phương trình đã được giảm xuống trong [8].

20p phalinh21 01-09-2011 45 5   Download