Large dynamics of Yang–Mills theory: mean dimension formula

Masaki Tsukamoto

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We study the Yang–Mills anti-self-dual (ASD) equation over the cylinder as a non-linear evolution equation. We consider a dynamical system consisting of bounded orbits of this evolution equation. This system contains many chaotic orbits, and moreover becomes an infinite dimensional and infinite entropy system. We study the mean dimension of this huge dynamical system. Mean dimension is a topological invariant of dynamical systems introduced by Gromov. We prove the exact formula of the mean dimension by developing a new technique based on the metric mean dimension theory of Lindenstrauss–Weiss.

Original languageEnglish
Pages (from-to)455-499
Number of pages45
JournalJournal d'Analyse Mathematique
Issue number2
Publication statusPublished - Feb 1 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics(all)


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