Special Session 45: Frontiers in Topological Dynamics: Theory, Applications, and Interdisciplinary Connections

Development of Bowen`s specification legacy on thermodynamic formalism and applications to stochastic properties
Tianyu Wang
School of Mathematical Sciences Shanghai Jiao Tong University
Peoples Rep of China
Co-Author(s):    
Abstract:
In 1970`s, Rufus Bowen proposed a general criterion on establishing thermodynamic formalism of a dynamical system by extracting critical features of a uniformly hyperbolic system equipped with a H\{o}lder continuous potential. Precisely, he showed that on an expansive homeomorphism satisfying a strong orbital concatenation property called specification, any boundedly distorted continuous potential must possess a unique equilibrium state. In this talk, we briefly survey the development of Bowen`s argument in the past two decades by illustrating how Bowen`s idea is extended to a variety of systems beyond compact uniform setting. This includes the introduction of a recent variant of Bowen`s approach, as well as its applications on detecting a few types of strong stochastic behaviors