Simplicial Dynamical Systems

Author

Ethan Akin, Missouri University of Science and TechnologyFollow

Abstract

A simplicial dynamical system is a simplicial map g : K* → K where K is a finite simplicial complex triangulating a compact polyhedron X and K* is a proper subdivision of K, e.g. the barycentric or any further subdivision. The dynamics of the associated piecewise linear map g : X → X can be analyzed by using certain naturally related subshifts of finite type. Any continuous map on X can be C⁰ approximated by such systems. Other examples yield interesting subshift constructions.

Recommended Citation

E. Akin, "Simplicial Dynamical Systems," Memoirs of the American Mathematical Society, vol. 140, no. 667, Americam Mathematical Society, Jan 1999.

The definitive version is available at https://doi.org/10.1090/memo/0667

Department(s)

Mathematics and Statistics

Keywords and Phrases

Basic sets; Hyperbolicity; Markov measures; Sample path spaces; Simplicial dynamics; Subshifts of finite type

International Standard Serial Number (ISSN)

0065-9266

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2026 Americam Mathematical Society, All rights reserved.

Publication Date

01 Jan 1999