2025/01/23 by Robin J. Deeley, Deeley, Robin J., Andrew M. Stocker +1
Computer Science · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #K-Theory and Homology (math.KT) #Nonlinear Dynamics and Pattern Formation #Operator Algebras (math.OA) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2501.13909
openalex publication_date 2025/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main goals of the present paper are to determine the structure of the C^∗-algebras associated to a finitely presented system and to develop the basic theory of the Ruelle algebras associated to a general synchronizing system. The later is related to the former in the sense that we show that Ruelle algebras associated to a finitely presented system are explicitly related to the Smale space case. The relevant C^∗-algebras are the synchronizing heteroclinic algebras that were introduced in our previous work on synchronizing systems. They are very much related to previous work of Thomsen, who in turn was building on work of Ruelle, Putnam, and Spielberg.