2017/12/06 by OLIVER JENKINSON, Oliver Jenkinson · 15 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Caveolin-1 and cellular processes #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation #math.DS
paper · pdf · doi:10.1017/etds.2017.142
published as Ergod. Th. Dynam. Sys. 39 (2019) 2593-2618 · Survey, to appear in Ergodic Theory & Dynamical Systems
arxiv created 2017/12/06 · openalex publication_date 2018/01/24 · arxiv updated 2019/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Ergodic optimization is the study of problems relating to maximizing orbits, maximizing invariant measures and maximum ergodic averages. An orbit of a dynamical system is called f-maximizing if the time average of the real-valued function f along the orbit is larger than along all other orbits, and an invariant probability measure is called f-maximizing if it gives f a larger space average than does any other invariant probability measure. In this survey we consider the main strands of ergodic optimization, beginning with an influential model problem, and the interpretation of ergodic optimization as the zero temperature limit of thermodynamic formalism. We describe typical properties of maximizing measures for various spaces of functions, the key tool of adding a coboundary so as to reveal properties of these measures, as well as certain classes of functions where the maximizing measure is known to be Sturmian.