Adversarial ergodic optimization
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909813876719616 |
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| author | Young, Aidan |
| author_facet | Young, Aidan |
| contents | In this article, we introduce an ergodic optimization problem inspired by information theory, which can be presented informally as follows: given a factor map $π: (X, T) \to (Y, S)$ of topological dynamical systems, and a continuous function $f \in C(X)$, what can be said about the extrema $$\sup_{y \in Y} \inf_{x \in π^{-1} \{y\}} \lim_{k \to \infty} \frac{1}{k} \sum_{j = 0}^{k - 1} f \left( T^j x \right) ? $$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14981 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adversarial ergodic optimization Young, Aidan Dynamical Systems In this article, we introduce an ergodic optimization problem inspired by information theory, which can be presented informally as follows: given a factor map $π: (X, T) \to (Y, S)$ of topological dynamical systems, and a continuous function $f \in C(X)$, what can be said about the extrema $$\sup_{y \in Y} \inf_{x \in π^{-1} \{y\}} \lim_{k \to \infty} \frac{1}{k} \sum_{j = 0}^{k - 1} f \left( T^j x \right) ? $$ |
| title | Adversarial ergodic optimization |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2408.14981 |