BibTeX
@MISC{Jenkinson_rotation,entropy,,
author = {Oliver Jenkinson},
title = {Rotation, Entropy, and Equilibrium States},
year = {}
}
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Abstract
. For a dynamical system (X; T ) and function f : X ! R d we consider the corresponding generalised rotation set. We present a new approach to studying the entropy of rotation vectors in terms of equilibrium states. We relate this to the lost and directional ergodic measures and directional entropy introduced by Geller & Misiurewicz [14]. If (X; T ) is a mixing subshift of finite type, and f is of summable variation, we prove that at interior points of the rotation set the (directional) entropy is attained by a (unique) lost measure, and at exposed points it is attained by a directional measure. This sharpens and extends results in [14]. At non-exposed boundary points we show this classification breaks down completely. Our approach yields a new proof of a result of Marcus & Tuncel [31] characterising the faces of the weight-persymbol polytope of a Markov chain. Contents 1. Introduction 2 2. Convex geometry 5 3. A family of equilibrium states 6 4. Subshifts of finite type 10 5. The ...
Keyphrases
equilibrium state finite type directional ergodic measure summable variation dynamical system marcus tuncel directional entropy directional measure non-exposed boundary point new approach weight-persymbol polytope new proof rotation vector geller misiurewicz markov chain interior point corresponding generalised rotation
