SMALL LIPSCHITZ PERTURBATION OF SCALAR MAPS
AND LYAPUNOV EXPONENT FOR LIPSCHITZ MAPS
Giuliano G. La Guardia, Leonardo Pires
State University of Ponta Grossa
Department of Mathematics and Statistics
Ponta Grossa - 84030-900, BRAZIL

Abstract

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.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 35
Issue: 6
Year: 2022

DOI: 10.12732/ijam.v35i6.1

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