Nonuniform dichotomic behavior: Lipschitz invariant manifolds for\n difference equations

2012/09/28 by António J. G. Bento, Bento, António J. G., César M. Silva +1
Mathematics · Medicine · #34D09 #37D10 #37D25 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1209.6589

openalex publication_date 2012/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain global and local theorems on the existence of invariant manifolds\nfor perturbations of non autonomous linear difference equations assuming a very\ngeneral form of dichotomic behavior for the linear equation. The results\nobtained include situations where the behavior is far from hyperbolic. We also\ngive several new examples and show that our result includes as particular cases\nseveral previous theorems.\n

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