Non-stationary normal forms for contracting extensions

2020/06/22 by Boris Kalinin, Kalinin, Boris · 1 citation
Mathematics · Physics and Astronomy · #34C20 #37C15 #37D20 #37D30 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2006.12662

openalex publication_date 2020/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present the theory of non-stationary normal forms for uniformly contracting smooth extensions with sufficiently narrow Mather spectrum. We give coherent proofs of existence, (non)uniqueness, and a description of the centralizer results. As a corollary, we obtain corresponding results for normal forms along an invariant contracting foliation. The main improvements over the previous results in the narrow spectrum setting include explicit description of non-uniqueness and obtaining results in any regularity above the precise critical level, which is especially useful for the centralizer. In addition to sub-resonance normal form, we also prove corresponding results for resonance normal form, which is new in the narrow spectrum setting.

Citations

• The theory of non-stationary normal forms
• Normal forms on contracting foliations: smoothness and homogeneous structure

Cited by

• Rigidity of strong and weak foliations

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