Thermodynamic Formalism for Random Weighted Covering Systems

Centro de Matemática da Universidade do Porto 

*** Zoominar in Dynamical Systems ***

 

Date. May 22, 11h00m

 

Speaker. Jason Atnip (University of New South Wales, Sydney)

 

Title. Thermodynamic Formalism for Random Weighted Covering Systems

 

Abstract. In this talk we develop a quenched thermodynamic formalism for random dynamical systems generated by countably branched, piecewise-monotone mappings of the interval that satisfy a random covering condition. We consider a general random contracting potential (in the sense of Liverani-Saussol-Vaienti) and we prove there exists a unique random conformal measure and a unique random equilibrium state for this potential. Further, we prove quasi-compactness of the associated transfer operator cocycle and exponential decay of correlations for the unique equilibrium state.

We will give several examples of our general theory. In particular, our results apply to random beta-transformations, random Gauss-Renyi maps, and random dynamics of non-uniformly expanding maps such as intermittent maps and maps with contracting branches.

 

Online Zoom meeting (Session will open some minutes before 11h00)
https://videoconf-colibri.zoom.us/j/96908488801?pwd=SkZGRlN0M3BZZ2pIbkZHRlZvRkxQQT09

Meeting ID: 969 0848 8801
Password: 750081

Date and Venue

Start Date

Speaker

Jason Atnip

Speaker's Institution

University of New South Wales

Area

Dynamical Systems