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Rate of mixing for equilibrium states in negative curvature and trees | | Anne Broise-Alamichel
; Jouni Parkkonen
; Frédéric Paulin
; | | Date: |
16 Oct 2020 | | Abstract: | 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. | | Source: | arXiv, 2010.08212 | | Services: | Forum | Review | PDF | Favorites | |
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