CODIMENSION 3 HOMOCLINIC BIFURCATION OF ORBIT FLIP WITH RESONANT EIGENVALUES CORRESPONDING TO THE TANGENT DIRECTIONS

DOI10.1142/S0218127404011880zbMath1072.37041OpenAlexW2085868801MaRDI QIDQ5311837

Tian-Si Zhang, De-Ming Zhu

Publication date: 29 August 2005

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127404011880

zbMATH Keywords

homoclinic orbitorbit-flip

Mathematics Subject Classification ID

Homoclinic and heteroclinic orbits for dynamical systems (37C29) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (18)

Bifurcation of rough heteroclinic loop with orbit and inclination flips ⋮ Codimension-3 bifurcations of a class of homoclinic loop with saddle-point ⋮ CODIMENSION 3 HETEROCLINIC BIFURCATIONS WITH ORBIT AND INCLINATION FLIPS IN REVERSIBLE SYSTEMS ⋮ The twisting bifurcations of double homoclinic loops with resonant eigenvalues ⋮ Non-resonance 3D homoclinic bifurcation with an inclination flip ⋮ BIFURCATIONS OF HOMOCLINIC ORBIT CONNECTING TWO NONLEADING EIGENDIRECTIONS ⋮ Homoclinic flip bifurcations accompanied by transcritical bifurcation ⋮ Existence of periodic orbits and shift-invariant curve sequences near multiple homoclinics ⋮ BIFURCATIONS OF GENERIC HETEROCLINIC LOOP ACCOMPANIED BY TRANSCRITICAL BIFURCATION ⋮ Weak type heterodimensional cycle bifurcation with orbit-flip ⋮ Bifurcations of double homoclinic flip orbits with resonant eigenvalues ⋮ HETERODIMENSIONAL CYCLE BIFURCATION WITH ORBIT-FLIP ⋮ Codimension 3 nontwisted double homoclinic loops bifurcations with resonant eigenvalues ⋮ Bifurcations of heterodimensional cycles with one orbit flip and one inclination flip ⋮ Codimension 2 bifurcations of double homoclinic loops ⋮ Bifurcations of heterodimensional cycles with two saddle points ⋮ NONRESONANT BIFURCATIONS OF HETEROCLINIC LOOPS WITH ONE INCLINATION FLIP ⋮ Codimension 2 reversible heteroclinic bifurcations with inclination flips

Cites Work

• Bifurcations of rough heteroclinic loop with two saddle points
• Homoclinic bifurcation at resonant eigenvalues
• Bifurcations of heteroclinic loops
• Constructing dynamical systems having homoclinic bifurcation points of codimension two
• Degenerated homoclinic bifurcations with higher dimensions
• Bifurcations of nontwisted heteroclinic loop.
• Bifurcations of rough heteroclinic loops with three saddle points
• Numerical unfoldings of codimension-three resonant homoclinic flip bifurcations
• Resonant homoclinic flip bifurcations

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