Lectures on Structural Stability in Dynamics

These lectures present results and problems on the characterization of structurally stable dynamics. We will shed light those which do not seem to depend on the regularity class (holomorphic or differentiable). Furthermore, we will present some links between the problems of structural stability in dynamical systems and in singularity theory.Comment: 30pages and 9 figure

Lyapunov exponent for Lipschitz maps

It is well-known that the Lyapunov exponent plays a fundamental role in dynamical systems. In this note, we propose an alternative definition of Lyapunov exponent in terms of Lipschitz maps, which are not necessarily differentiable. We show that the results which are valid to standard discrete dynamical systems are also valid in this new context. Therefore, this novel approach expands the range of applications of the dynamical systems theory.Comment: Accepted for publication in Nonlinear Dynamic

Sub-Riemannian geometry of non-differentiable bundles

We show that the Chow`s Theorem and an analogue of the Ball-Box Theorem from smooth Sub-Riemannian geometry holds true for a class of non-differentiable tangent subbundles that satisfy a geometric condition. In the final section of the paper we also give examples of such bundles and an application to dynamical systems