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A. J. Homburg, H. Kokubu and M. Krupa, “The Cusp Horseshoe and Its Bifurcations in the Unfolding of an Inclinication-Flip Homoclinic Orbit,” Ergodic Theory and Dynamical Systems, Vol. 14, No. 4, 1994, pp. 667-693. doi:10.1017/S0143385700008117

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.