Bifurcations of nontwisted heteroclinic loop.

DOI10.1007/BF02884181zbMath1120.37309OpenAlexW1486596179MaRDI QIDQ1589767

Qingping Tian, De-Ming Zhu

Publication date: 12 December 2000

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

Full work available at URL: https://doi.org/10.1007/bf02884181

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (17)

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 ⋮ BIFURCATIONS OF HOMOCLINIC ORBIT CONNECTING TWO NONLEADING EIGENDIRECTIONS ⋮ Bifurcations of Heteroclinic Loop with Twisted Conditions ⋮ Bifurcation of an orbit homoclinic to a hyperbolic saddle of a vector field in \(\mathbb{R}^4\) ⋮ Bifurcations of double homoclinic flip orbits with resonant eigenvalues ⋮ Codimension 3 nontwisted double homoclinic loops bifurcations with resonant eigenvalues ⋮ Codimension 2 bifurcations of double homoclinic loops ⋮ Homoclinic bifurcation of orbit flip with resonant principal 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 ⋮ Codimension 2 reversible heteroclinic bifurcations with inclination flips ⋮ Bifurcations of fine 3-point-loop in higher dimensional space ⋮ Bifurcations of rough heteroclinic loops with three saddle points

Cites Work

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• Exponential dichotomies, heteroclinic orbits, and Melnikov functions
• Bifurcations of heteroclinic loops
• Homoclinic bifurcation with codimension 3
• Degenerate and non-trivial hyperbolic polycycles with two vertices
• The Bifurcation of Homoclinic and Periodic Orbits from Two Heteroclinic Orbits
• Homoclinic and heteroclinic bifurcations of Vector fields
• Problems in homoclinic bifurcation with higher dimensions
• Exponential trichotomy and heteroclinic bifurcations

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