Genericity of trivial Lyapunov spectrum for Lp-cocycles derived from second order linear homogeneous differential equations

2023/01/12 by Dinis Amaro, Amaro, Dinis, Mário Bessa +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Nonlinear Dynamics and Pattern Formation

paper · pdf · doi:10.48550/arxiv.2301.04905

openalex publication_date 2023/01/12 · openalex created_date 2023/01/14 · openalex updated_date 2026/07/28

Abstract

Given an ergodic flow φ^t\colon M→ M defined on a probability space M we study a family of continuous-time kinetic linear cocycles associated to the solutions of the second order linear homogeneous differential equations x +α(φ^t(ω)) x+β(φ^t(ω))x=0, where the parameters α,β evolve along the φ^t-orbit of ω∈ M. Our main result states that for a generic subset of kinetic continuous-time linear cocycles, where generic means a Baire second category with respect to an L^p-like topology on the infinitesimal generator, the Lyapunov spectrum is trivial.

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