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Multi-Pulse Homoclinic Loops in Systems with a Smooth First Integral

In: Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

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  • Dmitry Turaev

    (Weierstrass Institut für Angewandte Analysis und Stochastik)

Abstract

We prove that the orbit-flip bifurcation in the systems with a smooth first integral (e.g. in the Hamiltonian ones) leads to appearance of infinitely many multi-pulse self-localized solutions. We give a complete description to this set in the language of symbolic dynamics and reveal the role played by special nonselflocalized solutions (e.g. periodic and heteroclinic ones) in the structure of the set of self-localized solutions. We pay a special attention to the superhomoclinic (“homoclinic to homoclinic”) orbits whose presence leads to a particularly rich structure of this set.

Suggested Citation

  • Dmitry Turaev, 2001. "Multi-Pulse Homoclinic Loops in Systems with a Smooth First Integral," Springer Books, in: Bernold Fiedler (ed.), Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, pages 691-716, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-56589-2_28
    DOI: 10.1007/978-3-642-56589-2_28
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