Conditions Implying Annular Chaos: Quantitative results and Computer Assisted Proofs

2025/06/07 by Maciej J. Capiński, Maik Gröger, Capiński, M. J. +5 · 1 citation
Mathematics · Physics and Astronomy · #37B40 #37E30 #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2506.06608

openalex publication_date 2025/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive quantitative sufficient conditions for rotational chaos and diffusion in annular homeomorphisms, building on the topological criteria established in [31]. These conditions depend only on basic properties of the maps, making their implementation straightforward. To demonstrate the effectiveness of the method, we provide computer-assisted proofs of rotational chaos and diffusion for classical families of annular maps and their variations, in both conservative (twist and non-twist) and dissipative settings.

Citations

• Conditions implying annular chaos
• Topological horseshoes for surface homeomorphisms
• An elementary proof of a Theorem by Matsumoto
• Realizing rotation numbers on annular continua
• Forcing theory for transverse trajectories of surface homeomorphisms
• A characterization of annularity for area-preserving toral homeomorphisms
• Area-preserving diffeomorphisms of the torus whose rotation sets have\n non-empty interior
• On torus homeomorphisms whose rotation set is an interval
• A toral diffeomorphism with a nonpolygonal rotation set
• Rotation Sets for Maps of Tori

Cited by

• Birkhoff attractors for dissipative symplectic billiards

Related

• Conditions implying annular chaos
• Rotation Numbers and Instability Sets
• Applications of Forcing Theory to Homeomorphisms of the Closed Annulus
• Irrational rotation factors for conservative torus homeomorphisms
• Rotation sets of invariant separating continua of annular homeomorphisms