Bifurcations of rough heteroclinic loop with two saddle points

DOI10.1007/BF02884018zbMath1215.37039MaRDI QIDQ547815

De-Ming Zhu, Yin Lai Jin

Publication date: 25 June 2011

Published in: Science in China. Series A (Search for Journal in Brave)

zbMATH Keywords

local coordinatesPoincaré map1-homoclinic loop1-periodic orbit2-fold 1-periodic orbitbifurcation surface

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (23)

Bifurcation of rough heteroclinic loop with orbit and inclination flips ⋮ 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 ⋮ The twisting bifurcations of double homoclinic loops with resonant eigenvalues ⋮ Bifurcations of a homoclinic orbit to saddle-center in reversible systems ⋮ Degenerate orbit flip homoclinic bifurcations with higher dimensions ⋮ BIFURCATIONS OF HOMOCLINIC ORBIT CONNECTING TWO NONLEADING EIGENDIRECTIONS ⋮ Bifurcations of Heteroclinic Loop with Twisted Conditions ⋮ BIFURCATIONS OF GENERIC HETEROCLINIC LOOP ACCOMPANIED BY TRANSCRITICAL BIFURCATION ⋮ Bifurcations of double homoclinic flip orbits with resonant eigenvalues ⋮ Codimension 3 nontwisted double homoclinic loops bifurcations with resonant eigenvalues ⋮ Degenerate bifurcations of nontwisted heterodimensional cycles with codimension 3 ⋮ Bifurcations and stability of nondegenerated homoclinic loops for higher dimensional systems ⋮ 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 ⋮ Homoclinic bifurcation of orbit flip with resonant principal eigenvalues ⋮ Bifurcations of heteroclinic loops with nonresonant eigenvalues ⋮ Bifurcations of twisted heteroclinic loop with resonant eigenvalues ⋮ Codimension-4 resonant homoclinic bifurcations with orbit flips and inclination flips ⋮ NONRESONANT BIFURCATIONS OF HETEROCLINIC LOOPS WITH ONE INCLINATION FLIP ⋮ Bifurcations of fine 3-point-loop in higher dimensional space

Cites Work

• Homoclinic bifurcation at resonant eigenvalues
• Bifurcations of heteroclinic loops
• Degenerate and non-trivial hyperbolic polycycles with two vertices
• Degenerated homoclinic bifurcations with higher dimensions
• Bifurcations of rough heteroclinic loops with three saddle points
• On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
• Problems in homoclinic bifurcation with higher dimensions
• Bifurcation Theory and Methods of Dynamical Systems
• Exponential trichotomy and heteroclinic bifurcations
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