Unbounded dynamics for vector fields

2025/02/12 by Eran Igra, Igra, Eran
Mathematics · Physics and Astronomy · #34A26 #34A34 #34C05 #34C11 #34C45 #Advanced Differential Equations and Dynamical Systems #Chaos control and synchronization #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2502.08300

openalex publication_date 2025/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider a three-dimensional vector field F which generates a finite number of fixed points - what can we say on its unbounded dynamics? In this paper we tackle this question, and prove sufficient conditions for F to have fixed points with unbounded invariant manifolds. Following that, we use these results to study the dynamics of the Genesio-Tesi system, the Belousov-Zhabotinsky reaction, and the Michelson system.

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