Article citationsMore>>

M. V. Shashkov and D. V. Turaev, “An Existence Theorem of Smooth Nonlocal Center Manifolds for Systems Close to a System with a Homoclinic Loop,” Journal of Nonlinear Science, Vol. 9, No. 5, 1999, pp. 525-573. doi:10.1007/s003329900078

has been cited by the following article:

• TITLE: Resonant Homoclinic Bifurcations with Orbit Flips and Inclination Flips

  AUTHORS: Tiansi Zhang

  KEYWORDS: Orbit Flip; Inclination Flip; Resonance

  JOURNAL NAME: Applied Mathematics, Vol.4 No.2, February 22, 2013

  ABSTRACT: Homoclinic bifurcation with one orbit flip, two inclination flips and resonance in the tangent directions of homoclinic orbit is considered. By studying the associated successor functions constructed from a local active coordinate system, we prove the existence of double 1-periodic orbit, 1-homoclinic orbit, and also some coexistence conditions of 1-periodic orbit and 1-homoclinic orbit.