Article citationsMore>>

J. A. Yorke and K. T. Alligood, “Cascades of Period Doubling Bifurcations: A Prerequisite for Horseshoes,” Bulletin of the American Mathematical Society, Vol. 9, 1983, pp. 319-322. doi:10.1090/S0273-0979-1983-15191-1

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.