Global aspects of homoclinic bifurcations of three-dimensional saddles

DOI10.1016/0960-0779(93)90019-WzbMath0785.58036OpenAlexW2050315416MaRDI QIDQ2366784

Yun-Tung Lau

Publication date: 23 August 1993

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0960-0779(93)90019-w

zbMATH Keywords

homoclinic bifurcationsmanifold approachthree-dimensional global flowstime-delay functions

Mathematics Subject Classification ID

Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (3)

Non-resonance 3D homoclinic bifurcation with an inclination flip ⋮ Codimension 3 nontwisted double homoclinic loops bifurcations with resonant eigenvalues ⋮ Codimension 2 bifurcations of double homoclinic loops

Cites Work

• Unnamed Item
• Unnamed Item
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Local and global behavior near homoclinic orbits
• Bifurcation phenomena near homoclinic systems: A two-parameter analysis
• The Sil'nikov problem, exponential expansion, strong \(\lambda\)-lemma, \(C^ 1\)-linearization, and homoclinic bifurcation
• A strange family of three-dimensional vector fields near a degenerate singularity
• Global bifurcations and chaos. Analytical methods
• Dynamics of a three-dimensional incompressible flow with stagnation points
• The Lorenz equations: bifurcations, chaos, and strange attractors
• THE "COCOON" BIFURCATIONS IN THREE-DIMENSONAL SYSTEMS WITH TWO FIXED POINTS
• The Lorenz System: II. The Homoclinic Convolution of the Stable Manifolds
• ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. II
• ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. I

This page was built for publication: Global aspects of homoclinic bifurcations of three-dimensional saddles