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Three Dimensional Flows: From Hyperbolicity to Quasi-Stochasticity

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Book cover Dynamics, Games and Science

Part of the book series: CIM Series in Mathematical Sciences ((CIMSMS,volume 1))

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Abstract

In the present survey, we give an overview of some recent developments on examples of differential equations whose flows have heteroclinic cycles and networks; we fit some properties of their nonwandering sets into the classic theory of hyperbolic and pseudo-hyperbolic sets.

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Acknowledgements

The author would like to express his gratitude to the referees for their helpull comments and also to Isabel Labouriau and Mário Bessa for suggestions and encouragement. CMUP is supported by the European Regional Development Fund through the programme COMPETE and by the Portuguese Government through the Fundação para a Ciência e a Tecnologia (FCT) under the project PEst-C/MAT/UI0144/2011. The author was supported by the grant with reference SFRH/BPD/84709/2012 of FCT.

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  1. Centro de Matemática da Universidade do Porto and Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169–007, Porto, Portugal

    Alexandre A. P. Rodrigues

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  1. Alexandre A. P. Rodrigues
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Correspondence to Alexandre A. P. Rodrigues .

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  1. IHES Le Bois-Marie, Bures-sur-Yvette, France

    Jean-Pierre Bourguignon

  2. Department of Mathematics, ETH Zürich; Seminar für Angewandte Mathematik, Zürich, Switzerland

    Rolf Jeltsch

  3. Department of Mathematics, University of Porto; Faculty of Sciences, Porto, Portugal

    Alberto Adrego Pinto

  4. Instituto de Matemática Pura e Aplicada, IMPA, Rio de Janeiro, Rio de Janeiro, Brazil

    Marcelo Viana

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Rodrigues, A.A.P. (2015). Three Dimensional Flows: From Hyperbolicity to Quasi-Stochasticity. In: Bourguignon, JP., Jeltsch, R., Pinto, A., Viana, M. (eds) Dynamics, Games and Science. CIM Series in Mathematical Sciences, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-16118-1_31

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