On systems with separatrix contour containing two saddle-foci.

DOI10.1007/BF02169052zbMath1160.37377OpenAlexW2064941845MaRDI QIDQ1125639

V. V. Bykov

Publication date: 12 December 1999

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02169052

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Singularities of vector fields, topological aspects (58K45) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (13)

Dissecting a resonance wedge on heteroclinic bifurcations ⋮ Dynamics of conservative Bykov cycles: tangencies, generalized Cocoon bifurcations and elliptic solutions ⋮ Using Lin's method to solve Bykov's problems ⋮ Time averages and periodic attractors at high Rayleigh number for Lorenz-like models ⋮ Analysis of the T-point-Hopf bifurcation in the Lorenz system ⋮ Dense heteroclinic tangencies near a Bykov cycle ⋮ Global bifurcations close to symmetry ⋮ Analysis of the T-point-Hopf bifurcation ⋮ ANALYSIS OF THE T-POINT–HOPF BIFURCATION WITH ℤ₂-SYMMETRY: APPLICATION TO CHUA'S EQUATION ⋮ Complete set of invariants for a Bykov attractor ⋮ Existence of homoclinic connections in continuous piecewise linear systems ⋮ Heteroclinic bifurcations near Hopf-zero bifurcation in reversible vector fields in \(\mathbb R^3\) ⋮ Ordered intricacy of Shilnikov saddle-focus homoclinics in symmetric systems

Cites Work

• Unnamed Item
• The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
• The bifurcations of separatrix contours and chaos
• ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. II

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