Minimax aspects of optimizations in ergodic theory

We study optimization problems in ergodic theory from the view point of minimax problems. We give minimax characterizations of maximum ergodic averages involving time averages. Our approach works for the abstract variational principle of generalized pressure functions which is proved by Bi\'{s}...

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Bibliographic Details
Published in:arXiv.org 2024-12
Main Author: Motonaga, Shoya
Format: Article
Language:English
Subjects:
Minimax technique
Online Access:Get full text
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Summary:We study optimization problems in ergodic theory from the view point of minimax problems. We give minimax characterizations of maximum ergodic averages involving time averages. Our approach works for the abstract variational principle of generalized pressure functions which is proved by Bi\'{s} et al. (2022). We also describe the relationship between our minimax results and the Fenchel-Rockafellar duality.
ISSN:2331-8422