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Repelling Dynamics Near a Bykov Cycle

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Abstract

What set does an experimenter see while he simulating numerically the dynamics near a Bykov cycle? In this paper, we discuss the fate of typical trajectories near a Bykov cycle for a \(C^1\)-vector field and we establish that despite the existence of shift dynamics (chaos) nearby, Lebesgue—almost all trajectories starting in a small neighbourhood of a Bykov cycle are repelled.

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Notes

  1. In our case, they are smooth.

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Acknowledgments

The author would like to express his gratitude to Isabel Labouriau and Mário Bessa for helpful discussions. 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. A.A.P. Rodrigues was supported by the grant SFRH/BPD/84709/2012

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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, Porto, 4169-007, Portugal

    Alexandre A. P. Rodrigues

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Correspondence to Alexandre A. P. Rodrigues.

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Rodrigues, A.A.P. Repelling Dynamics Near a Bykov Cycle. J Dyn Diff Equat 25, 605–625 (2013). https://doi.org/10.1007/s10884-013-9289-2

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  • DOI: https://doi.org/10.1007/s10884-013-9289-2

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