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A Note on Discontinuous Vector Fields and Reversible Mappings

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Dynamics, Bifurcation and Symmetry

Part of the book series: NATO ASI Series ((ASIC,volume 437))

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Abstract

The purpose of this note is to present an elementary discussion of the dynamic behavior of both reversible mappings and ordinary differential equations with discontinuous right-hand sides. We explore the main ideas and results needed for the qualitative study of such ODE through reversible mappings. The key of the problem is that, under certain conditions, reversible mappings work as first return mappings associated to the equations.

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References

  1. - A.A. Andronov et al, Theory of oscillators, Dover, NY, 1987.

    Google Scholar 

  2. - E. Barbashin, Introduction to the theory of stability, Noordhoff, Groningen, 1970.

    MATH  Google Scholar 

  3. - A.F. Filippov, Differencial equations with discontinuous righ-hand sides, Kluwer, 1988.

    Google Scholar 

  4. - MA. Teixeira, Generic bifurcation of discontinuous vector fields, An. Acad. Bras. Cienc., V. 53 (2) 1981.

    Google Scholar 

  5. -MA. Teixeira, Local and simultaneous structural stability of certain diffeomor-phisms, Springer-Verlag Lecture Notes, V. 898, 1982.

    Google Scholar 

  6. -MA. Teixeira, On topological stability of divergent diagrams of folds, Math. Z., V.180,1982.

    Google Scholar 

  7. ] - MA. Teixeira, A topological invariant for discontinuous vector fields, Nonlinear Anal.: TMA, V. 9, 1985.

    Google Scholar 

  8. -MA. Teixeira, Stability conditions for discontinuous vector fields, J. Diff. Eq., V.88 (1), 1990.

    Google Scholar 

  9. - S. M. Voronin, Analytic classification of pairs of involutions and its applications, Funktional’nyi Anaiz Prilozheniya, V. 16, N. 2, 1982.

    MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Imecc - Unicamp, Brazil

    Marco A. Teixeira

Authors
  1. Marco A. Teixeira
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Editor information

Editors and Affiliations

  1. Institut Non Linéaire de Nice, CNRS — Université de Nice, Sophia Antipolis, France

    Pascal Chossat

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© 1994 Springer Science+Business Media Dordrecht

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Teixeira, M.A. (1994). A Note on Discontinuous Vector Fields and Reversible Mappings. In: Chossat, P. (eds) Dynamics, Bifurcation and Symmetry. NATO ASI Series, vol 437. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0956-7_24

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  • DOI: https://doi.org/10.1007/978-94-011-0956-7_24

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4413-4

  • Online ISBN: 978-94-011-0956-7

  • eBook Packages: Springer Book Archive

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