Open AccessResonant Homoclinic Bifurcations with Orbit Flips and Inclination Flips
Author(s) -
Tiansi Zhang
Publication year - 2013
Publication title -
applied mathematics
Language(s) - English
Resource type - Journals
eISSN - 2152-7393
pISSN - 2152-7385
DOI - 10.4236/am.2013.42042
Subject(s) - homoclinic orbit , heteroclinic orbit , homoclinic bifurcation , orbit (dynamics) , tangent , bifurcation , physics , circular orbit , mathematics , mathematical analysis , classical mechanics , geometry , nonlinear system , quantum mechanics , engineering , aerospace engineering
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.