Codimension-4 resonant homoclinic bifurcations with orbit flips and inclination flips

DOI10.1007/s10114-015-2456-0zbMath1371.37035OpenAlexW1056177206MaRDI QIDQ2516019

De-Ming Zhu, Tian-Si Zhang

Publication date: 10 August 2015

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-015-2456-0

zbMATH Keywords

inclination fliporbit flipresonanthomoclinic-doubling bifurcation

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Cites Work

• Bifurcations of rough heteroclinic loop with two saddle points
• Bifurcations of heteroclinic loops
• Homoclinic tangencies near cascades of period doubling bifurcations
• Bifurcations of nontwisted heteroclinic loop.
• Homoclinic flip bifurcations accompanied by transcritical bifurcation
• Homoclinic bifurcation of orbit flip with resonant principal eigenvalues
• Inclination-flip homoclinic orbits arising from orbit-flip
• Numerical unfoldings of codimension-three resonant homoclinic flip bifurcations
• Cascades of period-doubling bifurcations: A prerequisite for horseshoes
• BIFURCATIONS OF HOMOCLINIC ORBIT CONNECTING TWO NONLEADING EIGENDIRECTIONS
• BIFURCATIONS OF GENERIC HETEROCLINIC LOOP ACCOMPANIED BY TRANSCRITICAL BIFURCATION
• HETERODIMENSIONAL CYCLE BIFURCATION WITH ORBIT-FLIP
• MULTIPLE HOMOCLINIC BIFURCATIONS FROM ORBIT-FLIP I: SUCCESSIVE HOMOCLINIC DOUBLINGS
• Homoclinic-doubling cascades.

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