On the dynamics of minimal homeomorphisms of \mathbbT² which are not pseudo-rotations

2016/11/11 by Alejandro Kocsard, Kocsard, Alejandro
Mathematics · #37E30 #37E45 #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1611.03784

openalex publication_date 2016/11/11 · openalex created_date 2017/01/06 · openalex updated_date 2026/07/28

Abstract

We prove that any minimal 2-torus homeomorphism which is isotopic to the identity and whose rotation set is not just a point exhibits uniformly bounded rotational deviations on the perpendicular direction to the rotation set. As a consequence of this, we show that any such homeomorphism is topologically mixing and we prove Franks-Misiurewicz conjecture under the assumption of minimality.

Citations

• Forcing theory for transverse trajectories of surface homeomorphisms
• Rotation Sets for Maps of Tori
• Recurrence of Co-Cycles and Random Walks

Related

• The Franks-Misiurewicz conjecture for extensions of irrational rotations
• Fully chaotic conservative models for some torus homeomorphisms
• Forcing theory for transverse trajectories of surface homeomorphisms
• On Stable and Unstable Behaviours of Certain Rotation Segments
• Rotation sets and almost periodic sequences