Topological isomorphism for rank-1 systems

2012/07/19 by Aaron Hill, Gao, Su, Hill, Aaron
Computer Science · Mathematics · #03E15 #37B10 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1207.4527

openalex publication_date 2012/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define the Polish space R of non-degenerate rank-1 systems. Each non-degenerate rank-1 system can be viewed as a measure-preserving transformation of an atomless, σ-finite measure space and as a homeomorphism of a Cantor space. We completely characterize when two non-degenerate rank-1 systems are topologically isomorphic. We also analyze the complexity of the topological isomorphism relation on R, showing that it is F_σ as a subset of R × R and bi-reducible to E₀. We also explicitly describe when a non-degenerate rank-1 system is topologically isomorphic to its inverse.

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