Non Quasi-Periodic Normal Form Theory

2023/03/17 by Gabriella Pinzari, Pinzari, Gabriella
Mathematics · Physics and Astronomy · #(2010): 37J40 #37J05 #37J10 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods for differential equations #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2303.10143

openalex publication_date 2023/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We review a recent generalization of Normal Form Theory to systems (Hamiltonian ones or general ODEs) where the perturbing term is not periodic in one coordinate variable. The main difference with the standard case relies on the non uniqueness of the Normal Form and the total absence of the small divisors problem. The exposition is quite general, so as to allow extensions to the case of more non--periodic coordinates, and more functional settings. Here, for simplicity, we work in the real--analytic class.

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