H. Kokubu, M. Komuru and H. Oka, “Multiple Homoclinic Bifurcations from Orbit Flip I. Sucessive Homoclinic Doublings,” International Journal of Bifurcation and Chaos, Vol. 6, No. 5, 1996, pp. 833-850. doi:10.1142/S0218127496000461

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.