# Strong regularity

## TL;DR

This book introduces the concept of strong regularity in dynamical systems, presenting key proofs and comparing methods for analyzing non-uniform hyperbolicity in low-dimensional systems.

## Contribution

It compiles and compares major proofs related to strong regularity and non-uniform hyperbolicity, providing a comprehensive overview of recent advances in the field.

## Key findings

- Yoccoz's proof of Jakobson theorem included
- Berger's proof on non-uniform hyperbolic Hénon-like maps presented
- Comparison of binding and strong regularity methods provided

## Abstract

This is an introduction of a book called "strong regularity", to appear at Ast\'erisque, containing: 1) Yoccoz' proof of Jakobson theorem www.college-de-france.fr/media/jean-christophe-yoccoz/UPL7416254474776698194_Jakobson_jcy.pdf 2) Berger's proof of the abundance of non-uniformly hyperbolic H\'enon like endomorphisms arxiv.org/abs/0903.1473 It gives an overview of the main examples and conjectures of non-uniformly hyperbolic set for low dimensional dynamical systems. It compares the proofs of parameter selections based on the concept of binding with those based on the one of strong regularity.