Computer assisted proofs for hyperbolic quasi-periodic invariant tori in dissipative twist maps

2023/05/08 by Victor Linroth, Linroth, Victor
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Numerical Analysis (math.NA) #Quantum chaos and dynamical systems #Scientific Research and Discoveries

paper · pdf · doi:10.48550/arxiv.2305.04640

openalex publication_date 2023/05/08 · openalex created_date 2023/05/10 · openalex updated_date 2026/07/28

Abstract

This paper outlines an approach for proving existence of hyperbolic quasi-periodic invariant tori using computer assisted methods based on an a posteriori KAM-like theorem. We implement it for the dissipative standard map following the approach and give computer assisted proofs of existence of invariant circles for some parameter choices.

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