Lyapunov exponent for Lipschitz maps
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It is well known that the Lyapunov exponent plays a fundamental role in dynamical systems. In this note, we propose a definition of Lyapunov exponent for Lipschitz maps, which are not necessarily differentiable. Additionally, we show that the main results which are valid to discrete standard dynamical systems are also true when considering Lipschitz maps instead of considering differentiable maps. Therefore, this novel approach expands the theory of dynamical systems.
KeywordsLyapunov exponent Lipschitz maps
This research has been partially supported by the Brazilian Agencies CAPES and CNPq. We would like to thank the anonymous referees for their valuable suggestions and comments that helped to improve significantly the quality and the readability of this paper, and Prof. Antonio Marcos Batista for helpful discussions. We also would like to thank the Associate Editor Stefano Lenci and the Editor-in-Chief Walter Lacarbonara for their excellent works on the review process. The authors declare that there is not conflict of interests in the publication of this paper.