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An example of Silnikov focus-focus homoclinic orbits

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Publication:2202222
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DOI10.1016/j.na.2020.112110zbMath1483.34060OpenAlexW3082538010MaRDI QIDQ2202222

Flaviano Battelli, Kenneth James Palmer

Publication date: 17 September 2020

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2020.112110



Mathematics Subject Classification ID

Complex behavior and chaotic systems of ordinary differential equations (34C28) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)




Cites Work

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  • A computable criterion for the existence of connecting orbits in autonomous dynamics
  • A remark about Sil'nikov saddle-focus homoclinic orbits
  • On Shilnikov's homoclinic-saddle-focus theorem
  • Bifurcation to homoclinic connections of the focus-saddle type
  • Elements of applied bifurcation theory.
  • Exponential dichotomies and transversal homoclinic points
  • The Numerical Computation of Connecting Orbits in Dynamical Systems
  • A CONTRIBUTION TO THE PROBLEM OF THE STRUCTURE OF AN EXTENDED NEIGHBORHOOD OF A ROUGH EQUILIBRIUM STATE OF SADDLE-FOCUS TYPE


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