On the constructivity of the variational approach to Arnold's Diffusion

2023/06/20 by Alessandro Fortunati, Fortunati, Alessandro
Computer Science · Physics and Astronomy · #37J40 #37J50 #65K10 #70H08 #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2306.11834

openalex publication_date 2023/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

The aim of this paper is to discuss the constructivity of the method originally introduced by U. Bessi to approach the phenomenon of topological instability commonly known as Arnold's Diffusion. By adapting results and proofs from existing works and introducing additional tools where necessary, it is shown how, at least for a (well known) paradigmatic model, it is possible to obtain a rigorous proof on a suitable discrete space, which can be fully implemented on a computer. A selection of explicitly constructed diffusing trajectories for the system at hand is presented in the final section.

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