A Description of Natural Measures via Quasi-ergodicity

Transient chaos has been a recognized phenomenon in the mathematical physics literature since at least the works of Kantz and Grassberger in 1985. In order to understand and characterise transient chaos, several computational approaches have been developed to approximate the so called “natural measure” supported on repellers of a dynamical systems. In this talk we explore how we can use absorbing Markov chains, and in particular quasi-ergodic measures, to approximate natural measures for a wide range of systems where transient chaos is presented. This is a joint work with Bernat Bassols-Cornudella and Jeroen S. W. Lamb.