Large dynamics of Yang--Mills theory: mean dimension formula
arXiv:1407.2058
Abstract
This paper studies the Yang--Mills 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 it 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.
arXiv comment40 pages
References in corpus (5)
- Mean Dimension & Jaworski-type Theorems
- Dynamical Embedding in Cubical Shifts & the Topological Rokhlin and Small Boundary Properties
- Deux exemples sur la dimension moyenne d'un espace de courbes de Brody
- Mean Dimension, Mean Rank, and von Neumann-Lück Rank
- Local mean dimension of ASD moduli spaces over the cylinder