Lipschitz perturbations of the Chafee-Infante equation

Pires, Leonardo

doi:10.1016/j.jmaa.2022.126740

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2023

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Cited by 5 publications

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“…In both concepts, the notion of differentiability is required. However, dynamical systems generated by Lischitz functions, without differentiability requirement, have interesting qualitative properties as we can see in the works [2,3,4,5,10,11,14].…”

Section: Introductionmentioning

confidence: 99%

Small Lipschitz Perturbation of Scalar Maps and Lyapunov Exponent for Lipschitz Maps

Guardia¹,

Pires²

2023

Int. J. of Appl. Math.

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In this paper we consider small Lipschitz perturbations for Lipschitz maps. We obtain conditions to ensure the permanence of fixed points (sink and source) for scalar Lipschitz maps without requiring differentiability, in a step norm weaker than the C 1 -norm and stronger than the C 0 -norm. Moreover, we also propose conditions in order to guarantee the permanence of periodic points. Additionally, we propose a new definition of Lyapunov exponent for Lipschitz maps which extends, in a natural way, the definition of Lyapunov exponent for differentiable maps.

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