6533b851fe1ef96bd12aa08c

RESEARCH PRODUCT

Rate of Mixing for Equilibrium States in Negative Curvature and Trees

Jouni ParkkonenAnne Broise-alamichelFrédéric Paulin

subject

Pure mathematicssymbols.namesakeExponential growthDiscrete time and continuous timeThermodynamic equilibriumsymbolsCountable setNegative curvatureGibbs measureQuotientMathematicsExponential function

description

In this survey based on the recent book by the three authors, 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, emphasizing 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.

yearjournalcountryeditionlanguage
2021-01-01
https://doi.org/10.1007/978-3-030-74863-0_9