Parameterized families of strange attractors represented through inverse limits: topological and measure-theoretic aspects

This project aims to study topological, dynamical and ergodic 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 the fact that Hénon attractors have been known to mathematicians for more than 40 years, the topology of the attractors has not been studied in detail yet. The main obstacle that such a study has not been established yet was the lack of techniques necessary to perform it. Building on the 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.