Resonant Homoclinic Bifurcations with Orbit Flips and Inclination Flips | Zendy

Tiansi Zhang | Zendy

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Resonant 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.

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