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Bifurcations and Attractor-Repeller Splittings of Non-Saddle Sets

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Abstract

This paper is devoted to the study of some aspects of the stability theory of flows. In particular, we study Morse decompositions induced by non-saddle sets, including their corresponding Morse equations, attractor-repeller splittings of non-saddle sets and bifurcations originated by implosions of the basin of attraction of asymptotically stable fixed points. We also characterize the non-saddle sets of the plane in terms of the Euler characteristic of their region of influence.

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Acknowledgements

The authors are grateful to José M. Montesinos-Amilibia and Jaime J. Sá nchez Gabites for useful comments and inspiring conversations. They would also like to express their thanks to the referee, whose remarks have helped to improve the manuscript.

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Authors and Affiliations

  1. Facultad de C. C. Matemáticas, Universidad Complutense de Madrid, 28040, Madrid, Spain

    Héctor Barge & José M. R. Sanjurjo

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  1. Héctor Barge
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  2. José M. R. Sanjurjo
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Correspondence to José M. R. Sanjurjo.

Additional information

The authors are supported by MINECO (MTM2012-30719). The first author is also supported by the FPI Grant BES-2013-062675.

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Barge, H., Sanjurjo, J.M.R. Bifurcations and Attractor-Repeller Splittings of Non-Saddle Sets. J Dyn Diff Equat 30, 257–272 (2018). https://doi.org/10.1007/s10884-017-9569-3

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  • DOI: https://doi.org/10.1007/s10884-017-9569-3

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