Anti-classification results for conjugacy of diffeomorphisms on manifolds

2025/05/14 by Bo Peng, Peng, Bo
Mathematics · #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2505.09491

Abstract

We show that the topological conjugacy relation of diffeomorphisms on any manifold of dimension at least 2 is not classifiable by countable structures. This answers a question of Foreman and Gorodetski. We also prove that E₀ is reducible into the topological conjugacy relation of minimal diffeomorphisms on the 2-torus, which answers a question of Foreman.

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