Skip to main content

Hereroclinic bifurcation in banach spaces

  • 998 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 1331)

Abstract

We study conditions under which a unique periodic orbit is generated from a heteroclinic contour when we add an autonomous perturbation to parabolic equations and to retarded differential equation.

Keywords

  • Periodic Orbit
  • Saddle Point
  • Parabolic Equation
  • Unstable Manifold
  • Homoclinic Orbit

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. C.M. Blázquez., Bufurcation from a homoclinic orbit in parabolic differential equation. Proc. of the Royal Soc. of Edim., 103A, (1986).

    Google Scholar 

  2. C.M. Blázquez, E. Tuma., On the generalization of a periodic orbit from a homoclinic in parabolic differential equations. Preprint.

    Google Scholar 

  3. S.M. Chow, B. Deng., Homoclinic and heteroclinic bifurcations in Banach spaces. Preprint.

    Google Scholar 

  4. S.M. Chow, J.K. Hale, J. Mallet-Paret., An example of bifurcation to homoclinic orbits. J. Diff. Eqns. 37. (1980).

    Google Scholar 

  5. J.K. Hale, X.B. Lin., Heteroclinic orbits for retarded functional differential equations. L.C.D.S., Brown Univ. 84–39 (1984).

    Google Scholar 

  6. J.K. Hale., Theory of Functional Differential Equations. Springer-Verlag. (1977).

    Google Scholar 

  7. D. Henry., Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Maths. 840. Berlin, Springer-Verlag. (1981).

    MATH  Google Scholar 

  8. V.K. Melnikov., On the stability of the center for time periodic perturbations. Trans. Moscow Math. Soc. 12 (1). (1964).

    Google Scholar 

  9. L.P. Silnikov., On the generation of a periodic motion from trajectories doubly asymptotic to an equilibrium state of saddle type. Mat. Sbornik. Tom 77 (119) # 3. (1968).

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Blázquez, M., Tuma, E. (1988). Hereroclinic bifurcation in banach spaces. In: Bamón, R., Labarca, R., Palis, J. (eds) Dynamical Systems Valparaiso 1986. Lecture Notes in Mathematics, vol 1331. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083063

Download citation

  • DOI: https://doi.org/10.1007/BFb0083063

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50016-2

  • Online ISBN: 978-3-540-45889-0

  • eBook Packages: Springer Book Archive