Algebraic entropy of endomorphisms of M-sets

Abstract

The usual notion of algebraic entropy associates to every group (monoid) endomorphism a value estimating the chaos created by the self-map. In this paper, we study the extension of this notion to arbitrary sets endowed with monoid actions, providing properties and relating it with other entropy notions. In particular, we focus our attention on the relationship with the coarse entropy of bornologous self-maps of quasi-coarse spaces. While studying the connection, an extension of a classification result due to Protasov is provided.

Keywords

• monoid actions
• group actions
• algebraic entropy
• endomorphisms
• coarse spaces
• quasi-coarse spaces
• coarse entropy
• 22f05
• 20m75
• 51f30
• 54c70
• 54e15
• 20m99