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- W2537403334 abstract "In this paper, we study the ergodic theory of the geodesic flow on negatively curved geometrically finite manifolds. We prove that the measure-theoretical entropy is upper semicontinuous when there is no loss of mass. In the case where mass is lost, the critical exponents of parabolic subgroups of the fundamental group have a significant meaning. More precisely, the failure of upper-semicontinuity of the entropy is determined by the maximal parabolic critical exponent. We also study the pressure of positive Hölder-continuous potentials going to zero through the cusps. We prove that the pressure map $tmapsto P(tF)$ is differentiable until it undergoes a phase transition, after which it becomes constant. This description allows us, in particular, to compute the entropy of the geodesic flow at infinity." @default.
- W2537403334 created "2016-10-28" @default.
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- W2537403334 date "2017-06-28" @default.
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- W2537403334 title "Escape of mass and entropy for geodesic flows" @default.
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- W2537403334 doi "https://doi.org/10.1017/etds.2017.40" @default.
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