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Nonlinear Dynamics

, Volume 92, Issue 3, pp 1217–1224 | Cite as

Lyapunov exponent for Lipschitz maps

  • Giuliano G. La Guardia
  • Pedro Jeferson Miranda
Original Paper
  • 104 Downloads

Abstract

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.

Keywords

Lyapunov exponent Lipschitz maps 

Notes

Acknowledgements

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.

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Giuliano G. La Guardia
    • 1
  • Pedro Jeferson Miranda
    • 2
  1. 1.Department of Mathematics and StatisticsState University of Ponta Grossa (UEPG)Ponta GrossaBrazil
  2. 2.Department of PhysicsState University of Ponta Grossa (UEPG)Ponta GrossaBrazil

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