Induced topological pressure for countable state Markov shifts

Abstract

We introduce the notion of induced topological pressure for countable state Markov shifts with respect to a non-negative scaling function and an arbitrary subset of finite words. Firstly, the scaling function allows a direct access to important thermodynamical quantities, which are usually given only implicitly by certain identities involving the classically defined pressure. In this context we generalise Savchenko's definition of entropy for special flows to a corresponding notion of topological pressure and show that this new notion coincides with the induced pressure for a large class of Hölder continuous height functions not necessarily bounded away from zero. Secondly, the dependence on the subset of words gives rise to interesting new results connecting the Gurevi{\vc} and the classical pressure with exhausting principles for a large class of Markov shifts. In this context we consider dynamical group extentions to demonstrate that our new approach provides a useful tool to characterise amenability of the underlying group structure.

28 pages

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Cited by in corpus (8)

• Bowen's equations for upper metric mean dimension with potential
• Induced topological pressure for topological dynamical(to appear in JPM)
• Spectral dimensions of Krein--Feller operators and $L^q$-spectra
• Recurrence and pressure for group extensions
• A complex Ruelle-Perron-Frobenius theorem for infinite Markov shifts with applications to renewal theory
• Time change for flows and thermodynamic formalism
• Thermodynamic formalism for transient dynamics on the real line
• Escape rates for special flows and their higher order asymptotics