Realizing arbitrary d-dimensional dynamics by renormalization of C^d-perturbations of identity

2021/03/29 by Bassam Fayad, Fayad, Bassam, Maria Saprykina +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · doi:10.48550/arxiv.2103.15530

openalex publication_date 2021/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Any C^d conservative map f of the d-dimensional unit ball \mathbb B^d can be realized by renormalized iteration of a C^d perturbation of identity: there exists a conservative diffeomorphism of \mathbb B^d, arbitrarily close to identity in the C^d topology, that has a periodic disc on which the return dynamics after a C^d change of coordinates is exactly f.

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