Exponential trichotomy and heteroclinic bifurcations

DOI10.1016/0362-546X(95)00164-QzbMath0877.34037OpenAlexW2003886058MaRDI QIDQ5689184

De-Ming Zhu

Publication date: 14 December 1997

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(95)00164-q

zbMATH Keywords

saddle-node bifurcationshomoclinic/heteroclinic orbitsexponential trichotomy theory

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (19)

A Zabczyk type method for the study of the exponential trichotomy of discrete dynamical systems ⋮ Homoclinic bifurcation with nonhyperbolic equilibria ⋮ Degenerate orbit flip homoclinic bifurcations with higher dimensions ⋮ Admissibility and exponential trichotomy of dynamical systems described by skew-product flows ⋮ Bifurcations of Heteroclinic Loop with Twisted Conditions ⋮ Bifurcations of twisted homoclinic loops for degenerated cases ⋮ Discrete admissibility and exponential trichotomy of dynamical systems ⋮ Lyapunov function and exponential trichotomy on time scales ⋮ Input-output admissibility and exponential trichotomy of difference equations ⋮ Bifurcations of rough heteroclinic loop with two saddle points ⋮ Lyapunov-Schmidt reduction for unfolding heteroclinic networks of equilibria and periodic orbits with tangencies ⋮ Bifurcations of heteroclinic loops with nonresonant eigenvalues ⋮ Bifurcations of twisted heteroclinic loop with resonant eigenvalues ⋮ Bifurcations of heteroclinic loops ⋮ Problems in homoclinic bifurcation with higher dimensions ⋮ Transversal bounded solutions in systems with normal slow variables ⋮ Bifurcations of nontwisted heteroclinic loop. ⋮ 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
• Bifurcation of a homoclinic orbit with a saddle-node equilibrium
• Global bifurcations and chaos. Analytical methods
• Local and global bifurcations with nonhyperbolic equilibria
• Melnikov vector and heteroclinic manifolds
• Melnikov-type vectors and principal normals
• Exponential dichotomies and transversal homoclinic points
• Homoclinic Bifurcations with Nonhyperbolic Equilibria
• ON SYSTEMS WITH A SADDLE-FOCUS HOMOCLINIC CURVE
• The Bifurcations of Countable Connections from a Twisted Heteroclinic Loop
• Melnikov vector in higher dimensions
• Homoclinic Solutions for Autonomous Dynamical Systems in Arbitrary Dimension

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