Conjugacy in the Cantor Set Automorphism Group

Author

Ethan Akin, Missouri University of Science and TechnologyFollow

Abstract

We survey, and extend, results on the adjoint action of the home-omorphism group H(X) on the space of surjective continuous maps, Cs (X), where X is a Cantor set. We look also at the restriction of the action to various dynamically defined subsets of Cs (X), e. g. the sets of topologically transitive maps, chain transitive maps, chain mixing maps, etc. In each case, we consider whether there exist elements with a dense conjugacy class and if so, what the generic elements look like.

Recommended Citation

E. Akin, "Conjugacy in the Cantor Set Automorphism Group," Contemporary Mathematics, vol. 678, pp. 1 - 42, American Mathematical Society, Jan 2016.

The definitive version is available at https://doi.org/10.1090/conm/678/13639

Department(s)

Mathematics and Statistics

International Standard Serial Number (ISSN)

1098-3627; 0271-4132

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2026 American Mathematical Society, All rights reserved.

Publication Date

01 Jan 2016