Singular heteroclinic cycles

DOI10.1006/jdeq.1999.3691zbMath0954.34031OpenAlexW2080876631MaRDI QIDQ1975459

Ale Jan Homburg

Publication date: 23 January 2001

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.1999.3691

zbMATH Keywords

chaotic dynamicsperiodic orbithomoclinic orbitsaddle-nodecodimension two bifurcationsinclination flip bifurcationsShil'nikov variablessingular heteroclinic cycles

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (6)

Homoclinic bifurcation with nonhyperbolic equilibria ⋮ On the existence of bifocal heteroclinic cycles in a class of four-dimensional piecewise affine systems ⋮ Homoclinic flip bifurcations accompanied by transcritical bifurcation ⋮ Multiple homoclinic orbits in conservative and reversible systems ⋮ Exponential trichotomy and homoclinic bifurcation with saddle-center equilibrium ⋮ On the complexity of periodic and nonperiodic behaviors of a hysteresis-based electronic oscillator

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bifurcation of a homoclinic orbit with a saddle-node equilibrium
• Exponential expansion with Šil'nikov's saddle-focus
• Homoclinic bifurcation at resonant eigenvalues
• The Sil'nikov problem, exponential expansion, strong \(\lambda\)-lemma, \(C^ 1\)-linearization, and homoclinic bifurcation
• Strange attractors in saddle-node cycles: Prevalence and globality
• Bifurcations to \(N\)-homoclinic orbits and \(N\)-periodic orbits in vector fields
• The Bifurcation of Homoclinic and Periodic Orbits from Two Heteroclinic Orbits
• Homoclinic Bifurcations with Nonhyperbolic Equilibria
• ON SYSTEMS WITH A SADDLE-FOCUS HOMOCLINIC CURVE
• The Bifurcations of Countable Connections from a Twisted Heteroclinic Loop
• Finitely-smooth normal forms of local families of diffeomorphisms and vector fields
• Elementary graphics of cyclicity 1 and 2
• The cusp horseshoe and its bifurcations in the unfolding of an inclination-flip homoclinic orbit
• On inclination-flip homoclinic orbit associated to a saddle-node singularity
• ON DIMENSION OF NON-LOCAL BIFURCATIONAL PROBLEMS
• ON THE COMPLEX BIFURCATION SET FOR A SYSTEM WITH SIMPLE DYNAMICS
• EXPONENTIAL EXPANSION WITH PRINCIPAL EIGENVALUES
• Strange attractor in the unfolding of an inclination-flip homoclinic orbit
• Global aspects of homoclinic bifurcations of vector fields
• A non-transverse homoclinic orbit to a saddle-node equilibrium
• ON THE GENERATION OF A PERIODIC MOTION FROM TRAJECTORIES DOUBLY ASYMPTOTIC TO AN EQUILIBRIUM STATE OF SADDLE TYPE
• ON A POINCARÉ-BIRKHOFF PROBLEM
• Invariant manifolds
• Homoclinic-doubling cascades.

This page was built for publication: Singular heteroclinic cycles