Quantitative statistical properties of two-dimensional partially hyperbolic systems

TL;DR

This paper investigates the statistical properties of two-dimensional partially hyperbolic systems, aiming to develop a general theoretical framework and applying it to fast-slow systems.

Contribution

It introduces a general theory for 2D partially hyperbolic systems beyond skew products, with applications to fast-slow dynamics.

Findings

Established foundational statistical properties for a broad class of systems

Applied the theory successfully to fast-slow partially hyperbolic systems

Provided insights into the structure of partially hyperbolic dynamics

Abstract

We study a class of two dimensional partially hyperbolic systems, not necessarily skew products, trying to establish the germ of a general theory. To illustrate the scope of the theory, we apply our results to the case of fast-slow partially hyperbolic systems.