Expoentes de Lyapunov sobre campos vetoriais de classe C0 Lipschitz

Abstract

In this work we will present two tools that are used to determine the hyperbolic behavior of differentiable and non differentiable vector fields that preserve volume element, defined over riemannian manifolds with dimension 3 (smooth, compact and connected), which we will denote, respectively, by classical and new Lyapunov exponents. We will show some of the similarities and differences they present: the invariance of the new exponent along the orbit of almost every point in M and the density of the set of differentiable vector fields with zero Lyapunov exponent in the set of the C 0 Lipschitz vector fields that preserve volume element. Keywords