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Large dynamics of Yang–Mills theory: mean dimension formula

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan

    Masaki Tsukamoto

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  1. Masaki Tsukamoto
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Correspondence to Masaki Tsukamoto.

Additional information

This paper was supported by Grant-in-Aid for Young Scientists (B) 25870334 from JSPS.

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Tsukamoto, M. Large dynamics of Yang–Mills theory: mean dimension formula. JAMA 134, 455–499 (2018). https://doi.org/10.1007/s11854-018-0014-2

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  • DOI: https://doi.org/10.1007/s11854-018-0014-2

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