Topological pressure dimension for almost additive potentials

Liu, Lei; Gong, Huajun; Zhou, Xiaoyao

doi:10.1080/14689367.2016.1148120

Cited by 2 publications

(1 citation statement)

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“…The short review about almost additive and asymptotically additive sequences above is far from complete. Numerous other works have studied or used almost additive sequences (see for example [1,57,3,56,39,58,2,61]) and asymptotically additive sequences (see for example [19,55,60,42,54,49,48]). We also mention that recent works (for example [31,32,38,30,29]) considered such potential sequences on non-compact spaces, and an extension of our main result to such spaces will be proved in Section 4.3.…”

Section: Large Deviationsmentioning

confidence: 99%

Additive, almost additive and asymptotically additive potential sequences are equivalent

Cuneo

2019

Preprint

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Motivated by various applications and examples, the standard notion of potential for dynamical systems has been generalized to almost additive and asymptotically additive potential sequences, and the corresponding thermodynamic formalism, dimension theory and large deviations theory have been extensively studied in the recent years. In this paper, we show that every such potential sequence is actually equivalent to a standard (additive) potential in the sense that there exists a continuous potential with the same topological pressure, equilibrium states, variational principle, weak Gibbs measures, level sets (and irregular set) for the Lyapunov exponent and large deviations properties. In this sense, our result shows that almost and asymptotically additive potential sequences do not extend the scope of the theory compared to standard potentials, and that many results in the literature about such sequences can be recovered as immediate consequences of their counterpart in the additive case. A corollary of our main result is that all quasi-Bernoulli measures are weak Gibbs.

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