Self-similar Inverse Semigroups and Smale Spaces

Self-similar inverse semigroups are defined using automata theory. Adjacency semigroups of s-resolved Markov partitions of Smale spaces are introduced. It is proved that a Smale space can be reconstructed from the adjacency semigroup of its Markov partition, using the notion of the limit solenoid of a contracting self-similar semigroup. The notions of the limit solenoid and a contracting semigroup is described.

• Type: Journal
• Year: 2006
• Where: IJAC
• Authors: Volodymyr Nekrashevych
• Keywords: Adjacency Semigroup, IJAC 2006, Markov Partition, Semigroup