Adversarial ergodic optimization

2024/08/27 by Aidan Young, Young, Aidan · 1 citation
Engineering · #Dynamical Systems (math.DS) #FOS: Mathematics #Scheduling and Optimization Algorithms

paper · pdf · doi:10.48550/arxiv.2408.14981

openalex publication_date 2024/08/27 · openalex created_date 2024/09/21 · openalex updated_date 2026/07/28

Abstract

In this article, we introduce an ergodic optimization problem inspired by information theory, which can be presented informally as follows: given a factor map π: (X, T) → (Y, S) of topological dynamical systems, and a continuous function f ∈ C(X), what can be said about the extrema sup_{y ∈ Y} inf_x ∈ π^-1 \y\ lim_{k → ∞} (1)/(k) ∑_{j = 0}^{k - 1} f ( T^j x ) ?

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