Bifurcations of rough heteroclinic loops with three saddle points

DOI10.1007/s101140100139zbMath1010.34037OpenAlexW2019151760MaRDI QIDQ1601234

Yin Lai Jin, De-Ming Zhu

Publication date: 6 August 2002

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

Full work available at URL: https://doi.org/10.1007/s101140100139

zbMATH Keywords

periodic orbithomoclinic orbitlocal coordinatesheteroclinic loopbifurcation surface

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)

Related Items (17)

Twisted bifurcations and stability of homoclinic loop with higher dimensions ⋮ Codimension 3 non-resonant bifurcations of rough heteroclinic loops with one orbit flip ⋮ CODIMENSION 3 HOMOCLINIC BIFURCATION OF ORBIT FLIP WITH RESONANT EIGENVALUES CORRESPONDING TO THE TANGENT DIRECTIONS ⋮ CODIMENSION 3 HETEROCLINIC BIFURCATIONS WITH ORBIT AND INCLINATION FLIPS IN REVERSIBLE SYSTEMS ⋮ Non-resonance 3D homoclinic bifurcation with an inclination flip ⋮ Bifurcations of Heteroclinic Loop with Twisted Conditions ⋮ Weak type heterodimensional cycle bifurcation with orbit-flip ⋮ BIFURCATIONS OF 2-2-1 HETERODIMENSIONAL CYCLES UNDER TRANSVERSALITY CONDITION ⋮ HETERODIMENSIONAL CYCLE BIFURCATION WITH ORBIT-FLIP ⋮ Codimension 2 bifurcation of twisted double homoclinic loops ⋮ Bifurcations of rough heteroclinic loop with two saddle points ⋮ Bifurcations of heterodimensional cycles with one orbit flip and one inclination flip ⋮ Bifurcations of heterodimensional cycles with two saddle points ⋮ Homoclinic bifurcation of orbit flip with resonant principal eigenvalues ⋮ NONRESONANT BIFURCATIONS OF HETEROCLINIC LOOPS WITH ONE INCLINATION FLIP ⋮ Bifurcations of rough 3-point-loop with higher dimensions ⋮ Bifurcations of fine 3-point-loop in higher dimensional space

Cites Work

• Homoclinic bifurcation at resonant eigenvalues
• Bifurcations of heteroclinic loops
• Local and global bifurcations with nonhyperbolic equilibria
• Degenerated homoclinic bifurcations with higher dimensions
• Bifurcations of nontwisted heteroclinic loop.
• Problems in homoclinic bifurcation with higher dimensions
• Exponential trichotomy and heteroclinic bifurcations
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