Journal article
Pablo D. Carrasco, F. Rodriguez-Hertz
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APA
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Carrasco, P. D., & Rodriguez-Hertz, F. Thermodynamic formalism for Quasi-Morphisms: Bounded Cohomology and Statistics.
Chicago/Turabian
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Carrasco, Pablo D., and F. Rodriguez-Hertz. “Thermodynamic Formalism for Quasi-Morphisms: Bounded Cohomology and Statistics” (n.d.).
MLA
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Carrasco, Pablo D., and F. Rodriguez-Hertz. Thermodynamic Formalism for Quasi-Morphisms: Bounded Cohomology and Statistics.
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@article{pablo-a,
title = {Thermodynamic formalism for Quasi-Morphisms: Bounded Cohomology and Statistics},
author = {Carrasco, Pablo D. and Rodriguez-Hertz, F.}
}
For a compact negatively curved space, we develop a notion of thermodynamic formalism and apply it to study the space of quasi-morphisms of its fundamental group modulo boundedness. We prove that this space is Banach isomorphic to the space of Bowen functions corresponding to the associated Gromov geodesic flow, modulo a weak notion of Livsic cohomology.
The results include that each such unbounded quasi-morphism is associated with a unique invariant measure for the flow, and this measure uniquely characterizes the cohomology class. As a consequence,
we establish the Central Limit Theorem for any unbounded quasi-morphism with respect to Markov measures, the invariance principle, and the Bernoulli property of the associated equilibrium state.
The results include that each such unbounded quasi-morphism is associated with a unique invariant measure for the flow, and this measure uniquely characterizes the cohomology class. As a consequence,
we establish the Central Limit Theorem for any unbounded quasi-morphism with respect to Markov measures, the invariance principle, and the Bernoulli property of the associated equilibrium state.