A multiplicative ergodic theoretic characterization of relative equilibrium states
- Authors
- Antonioli, John; Hong, Soonjo; Quas, Anthony
- Issue Date
- 24-May-2023
- Publisher
- CAMBRIDGE UNIV PRESS
- Keywords
- relative thermodynamic formalism; multiplicative ergodic theory; transfer operators
- Citation
- ERGODIC THEORY AND DYNAMICAL SYSTEMS, v.43, no.5, pp.1455 - 1470
- Journal Title
- ERGODIC THEORY AND DYNAMICAL SYSTEMS
- Volume
- 43
- Number
- 5
- Start Page
- 1455
- End Page
- 1470
- URI
- https://scholarworks.bwise.kr/hongik/handle/2020.sw.hongik/27563
- DOI
- 10.1017/etds.2022.15
- ISSN
- 0143-3857
- Abstract
- In this article, we continue the structural study of factor maps between symbolic dynamical systems and the relative thermodynamic formalism. Here, one is studying a factor map from a shift of finite type X (equipped with a potential function) to a sofic shift Z, equipped with a shift-invariant measure nu. We study relative equilibrium states, that is, shift-invariant measures on X that push forward under the factor map to v which maximize the relative pressure: the relative entropy plus the integral of phi. In this paper, we establish a new connection to multiplicative ergodic theory by relating these factor triples to a cocycle of Ruelle-Perron-Frobenius operators, and showing that the principal Lyapunov exponent of this cocycle is the relative pressure; and the dimension of the leading Oseledets space is equal to the number of measures of relative maximal entropy, counted with a previously identified concept of multiplicity.
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