Rate of mixing for equilibrium states in negative curvature and trees

Autor:	Broise-Alamichel, Anne, Parkkonen, Jouni, Paulin, Frédéric
Rok vydání:	2020
Předmět:	Mathematics - Dynamical Systems 37D35 37D40 37A25 53C22 20E08 37B10
Druh dokumentu:	Working Paper
Popis:	In this survey based on the book by the authors [BPP], we recall the Patterson-Sullivan construction of equilibrium states for the geodesic flow on negatively curved orbifolds or tree quotients, and discuss their mixing properties, emphazising the rate of mixing for (not necessarily compact) tree quotients via coding by countable (not necessarily finite) topological shifts. We give a new construction of numerous nonuniform tree lattices such that the (discrete time) geodesic flow on the tree quotient is exponentially mixing with respect to the maximal entropy measure: we construct examples whose tree quotients have an arbitrary space of ends or an arbitrary (at most exponential) growth type. Comment: 20 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2010.08212 Zobrazit plný text záznamu View this record from Arxiv