Local density of diffeomorphisms with large centralizers

TL;DR

This paper constructs a specific open set of C^1-diffeomorphisms on any compact manifold where a dense subset has uncountably large centralizers, revealing complex symmetry structures.

Contribution

It introduces a new class of diffeomorphisms with uncountably large centralizers, expanding understanding of symmetry in dynamical systems.

Findings

Existence of open set of diffeomorphisms with uncountable centralizers

Dense subset of these diffeomorphisms have non-trivial symmetry groups

Results apply to any compact manifold

Abstract

Given any compact manifold M, we construct a non-empty open subset O of the space of C^1-diffeomorphisms of M and a dense subset D of O such that the centralizer of every diffeomorphism in D is uncountable, hence non-trivial.