Sydney Dynamics Group: Jason Atnip -- Thermodynamic Formalism for Random Weighted Covering Systems

Dear all, 

This week, Friday May 15, Jason Atnip (UNSW) will give a talk at 4pm via
Zoom.  
Zoom link: https://uni-sydney.zoom.us/j/91755867536 
Meeting ID: 917 5586 7536

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.  


I hope to see you all online.  
Lachlan