Uniform stability and chaotic dynamics in nonhomogeneous linear dissipative scalar ordinary differential equations

2022/12/08 by Juan Campos, Campos, Juan, Carmen Gloria Núñez +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2212.04303

openalex publication_date 2022/12/08 · openalex created_date 2022/12/22 · openalex updated_date 2026/07/28

Abstract

The paper analyzes the structure and the inner long-term dynamics of the invariant compact sets for the skewproduct flow induced by a family of time-dependent ordinary differential equations of nonhomogeneous linear dissipative type. The main assumptions are made on the dissipative term and on the homogeneous linear term of the equations. The rich casuistic includes the uniform stability of the invariant compact sets, as well as the presence of Li-Yorke chaos and Auslander-Yorke chaos inside the attractor.

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