Computer-aided proofs for non-hyperbolic dynamics and blenders . This project aims to develop methods to rigorously detect certain geometric structures in systems that are known to imply chaos and are

Description

Computer-aided proofs for non-hyperbolic dynamics and blenders . This project aims to develop methods to rigorously detect certain geometric structures in systems that are known to imply chaos and are robust under perturbation. Such structures include blenders and robust heterodimensional cycles and homoclinic tangencies. This project expects to generate new knowledge in the area of non hyperbolic dynamics utilising a novel combination of recent developments in Dynamical Systems and techniques from rigorous numerics. Expected outcomes of this project include an efficient computation platform aimed at detecting and verifying chaos-inducing objects in complex dynamical systems. This should provide significant benefits, such as an increased understanding of non-hyperbolic dynamical systems. . Scheme: Discovery Projects. Field: 0101 - Pure Mathematics. Lead: Prof Warwick Tucker