Thermodynamic Formalism for Countable Markov Shifts in Hyperbolic Dynamics: A Transfinite Spectral Approach
Year: 2025
Type: article
Abstract: Mathematical Applications of Science Fiction We present a rigorous derivation of the thermodynamicformalism for countable Markov shifts (CMS) with a spe-cific focus on potentials of summable variation and theirtransfinite extensions in non-compact settings. By construct-ing a generalized Ruelle Transfer Operator Lϕ acting ona scale of Banach spaces adapted to the countable alpha-bet topology, we establish the existence and uniqueness ofequilibrium states (Gibbs measures) under the conditionof finite Gurevich pressure. We prove a spectral gap prop-erty for the operator using a Lasota-Yorke type inequality,thereby demonstrating exponential decay of correlations.The analysis extends to the transfinite limit of thermody-namic variables, providing a robust framework for hyperbolicdynamics on non-compact manifolds.
Authors: Revista, Zen, MFC, 10
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7117876007
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