Ergodic properties and flexibility of Lyapunov exponents for partially hyperbolic flows

Abstract

This project is part of the thematic research project Geometry of control, dynamical and stochastic systems, process #2018/13481-0, and aims to develope tools to enable the study of ergodic properties of non-uniformly and partially hyperbolic flows. In particular we propose to develop a perturbation theory of Lyapunov exponents of partially hyperbolic flows and/or geodesic flows on negatively curved manifolds of nonconstant curvature, the development of blenders for flows, we propose an study of flows topologically semi-conjugate to Anosov flows and the study of ergodic criterions for partially hyperbolic flows in general. Besides applying the expected results to existing examples in the literature, we will look forward to create new examples (possibly of geodesic flows, on non-positively curved manifolds, with at least two zero Lyapunov exponents) of non-Anosov partially hyperbolic flows, revealing dynamical phenomenons not observed until now. (AU)