WIAS Preprint No. 559, (2000)

Multi-pulse homoclinic loops in systems with a smooth first integral


Authors

  • Turaev, Dmitry

2010 Mathematics Subject Classification

  • 37J45 37G20 37D05 37J30 37G30 37G05 34C20 34C37

Keywords

  • Hamiltonian dynamics, localized solution, orbit-flip, homoclinic bifurcation, hyperbolic set, superhomoclinic orbit

DOI

10.20347/WIAS.PREPRINT.559

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 non-selflocalized 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.

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