2013/09/30 by Yuki Yayama · 29 citations
Computer Science · Mathematics · Physics and Astronomy · #Absolute continuity #Bounded function #Cellular Automata and Applications #Combinatorics #Continuous function (set theory) #Ergodic theory #Function (biology) #Gibbs measure #Invariant (physics) #Invariant measure #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematical physics #Mathematics #Measurable function #Measure (data warehouse) #Physics #Quantum mechanics #Sequence (biology) #Sigma #Theoretical and Computational Physics #math.DS
paper · pdf · doi:10.1017/etds.2014.50
published in Ergodic Theory and Dynamical Systems 36(1), 276-309 (Cambridge University Press) · 33 pages, To appear in Ergodic Theory and Dynamical Systems
arxiv created 2014/07/03 · openalex publication_date 2014/08/11 · arxiv updated 2015/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Let (X,\itσX),(Y,\itσY) be one-sided subshifts and \itπ:X→ Y a factor map. Suppose that X has the specification property. Let \itμ be a unique invariant Gibbs measure for a sequence of continuous functions F=\log fn\n=1∞ on X , which is an almost additive potential with bounded variation. We show that \itπ\itμ is a unique invariant Gibbs measure for a sequence of continuous functions G=\log gn\n=1∞ on Y . When (X,\itσX) is a full shift, we characterize G and \itμ by using relative pressure. This G is a generalization of a continuous function found by Pollicott and Kempton in their work on factors of Gibbs measures for continuous functions. We also consider the following question: given a unique invariant Gibbs measure \itν for a sequence of continuous functions F2 on Y , can we find an invariant Gibbs measure \itμ for a sequence of continuous functions F1 on X such that \itπ\itμ=\itν ? We show that such a measure exists under a certain condition. In particular, if (X,\itσX) is a full shift and \itν is a unique invariant Gibbs measure for a function in the Bowen class, then there exists a preimage \itμ of \itν which is a unique invariant Gibbs measure for a function in the Bowen class.