PFSAIL · Parameterised Families of Strange Attractors described through Inverse Limits

This project aims to study topological and dynamical aspects of two dimensional paradigm of chaos called Hénon attractors and introduce new treatable parametrised family of strange attractors appearing in smooth dynamical systems. Despite Hénon attractors have been known to mathematicians for more than 40 years, the topology of the attractors has not been studied in details yet. The main obstacle that such a study has not been established was the lack of techniques necessary to perform it. Building on recent advances in describing parametrised families of strange attractors using inverse limits we will delve in such a detailed study and give new results on topological, dynamical and measure-theoretic features appearing in parametrised families of strange attractors. We will use methods and techniques from Topological, Smooth, Surface and Symbolic Dynamics as well as Continuum and Ergodic Theory.