Some results on perturbations of Lyapunov exponents

Some results on generalized exponents

A digraph G = (V; E) is primitive if, for some positive integer k, there is a u ! v walk of length k for every pair u; v of vertices of V. The minimum such k is called the exponent of G, denoted exp(G). The exponent of a vertex u 2 V , denoted exp(u), is the least integer k such that there is a u ! v walk of length k for each v 2 V. For a set X V , exp(X) is the least integer k such that for ea...

Lyapunov Exponents For Some Quasi-Periodic Cocycles

We consider SL(2,R)-valued cocycles over rotations of the circle and prove that they are likely to have Lyapunov exponents ≈ ± logλ if the norms of all of the matrices are ≈ λ. This is proved for λ sufficiently large. The ubiquity of elliptic behavior is also observed. Consider an area preserving diffeomorphism f of a compact surface. Assume that f is not uniformly hyperbolic, but that it has o...

Lyapunov Exponents For Some Quasi - Periodic

We consider SL(2; R)-valuedcocycles over rotations of the circle and prove that they are likely to have Lyapunov exponents log if the norms of all of the matrices are. This is proved for suuciently large. The ubiquity of elliptic behavior is also observed. Consider an area preserving diieomorphism f of a compact surface. Assume that f is not uniformly hyperbolic, but that it has obvious hyperbo...

Lectures on Lyapunov exponents

construction of vector fields with positive lyapunov exponents

in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...