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Mediterranean Journal of Mathematics

, Volume 1, Issue 2, pp 123–149 | Cite as

Fluctuation between Subsets of Evolutions Governed by Chaotic Systems

  • Jean-Pierre Aubin
  • Patrick Saint-Pierre
Original paper
  • 22 Downloads

Abstract

Some issues on fluctuation of solutions to Lorenz and Rossler systems, for instance, are related to viability kernels of subsets under continuous time systems, or in the case of Julia sets, for instance, under discrete time systems. It happens that viability kernels of subsets, capture basins of targets and the combination of the twos provide tools for the analysis of the local behavior around equilibria (local stable and unstable manifolds), the asymptotic behavior and the functuation of evolutions between two areas of a domain, etc. Since algorithms and softwares do exist for computing the viability kernels and the capture basins, as well as evolutions viable in the viability kernel until they converge to a target infinite time, we are able to localize fluctuation basins.

Mathematics Subject Classification (2000).

Primary 37F50 Secondary 28A80 

Keywords.

Lorenz attractor Fractals Fluctuation Viability kernel Chaos à la Saari Julia sets Mandelbrot function Hutchison maps 

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Copyright information

© Birkhäuser-Verlag 2004

Authors and Affiliations

  1. 1.Réseau de Recherche Viabilité Jeux, ContrôleUniversité Paris-DauphineParis Cedex 16France
  2. 2.Réseau de Recherche Viabilité Jeux, ContrôleUniversité Paris-DauphineParis Cedex 16France

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