Uniform rigidity sequences for weak mixing diffeomorphisms on \mathbbT²

2014/11/10 by Philipp Kunde, Kunde, Philipp
Mathematics · #37A05 #37B20 #37C05 #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1411.2638

openalex publication_date 2014/11/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper we will show that if a sequence of natural numbers satisfies a certain growth rate, then there is a weak mixing diffeomorphism on \mathbbT² that is uniformly rigid with respect to that sequence. The proof is based on a quantitative version of the Anosov-Katok-method with explicitly defined conjugation maps and the constructions are done in the C^∞-topology as well as in the real-analytic topology.

Citations

• Rigidity in topological dynamics
• On weakly mixing homeomorphisms of the two-torus that are uniformly rigid

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