Dynamics of conservative Bykov cycles: tangencies, generalized Cocoon bifurcations and elliptic solutions

DOI10.1016/j.jde.2016.03.040zbMath1360.37130arXiv1511.08648OpenAlexW2963439119MaRDI QIDQ281659

Alexandre A. P. Rodrigues, Mário Bessa

Publication date: 11 May 2016

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

Full work available at URL: https://arxiv.org/abs/1511.08648

zbMATH Keywords

heteroclinic bifurcationsBykov cycleCocoon bifurcationselliptic solutions

Mathematics Subject Classification ID

Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Bifurcations connected with nontransversal intersection in dynamical systems (37G25)

Related Items (2)

Unfolding a Bykov attractor: from an attracting torus to strange attractors ⋮ Global bifurcations close to symmetry

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Moduli for heteroclinic connections involving saddle-foci and periodic solutions
• Repelling dynamics near a Bykov cycle
• About the unfolding of a Hopf-zero singularity
• Using Lin's method to solve Bykov's problems
• Attractors and repellers near generic elliptic points of reversible maps
• Global generic dynamics close to symmetry
• Dense heteroclinic tangencies near a Bykov cycle
• Global bifurcations close to symmetry
• Stable periodic motions in systems close to a structurally unstable homoclinic curve
• A generic incompressible flow is topological mixing
• Homoclinic tangencies versus uniform hyperbolicity for conservative 3-flows
• Steady solutions of the Kuramoto-Sivashinsky equation
• Uniqueness of connecting orbits in the equation \(Y^{(3)}=Y^ 2-1\)
• T-points: A codimension two heteroclinic bifurcation
• On systems with separatrix contour containing two saddle-foci.
• Cohomology equations near hyperbolic points and geometric versions of Sternberg linearization theorem
• Persistence of homoclinic tangencies for area-preserving maps
• The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
• The bifurcations of separatrix contours and chaos
• Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective
• Diffeomorphisms with infinitely many sinks
• Spiralling dynamics near heteroclinic networks
• Heteroclinic bifurcations near Hopf-zero bifurcation in reversible vector fields in \(\mathbb R^3\)
• New aspects in the unfolding of the nilpotent singularity of codimension three
• Partial Symmetry Breaking and Heteroclinic Tangencies
• Cascades of period-doubling bifurcations: A prerequisite for horseshoes
• Abundance of elliptic dynamics on conservative three-flows
• Switching near a network of rotating nodes
• Traveling waves on fluid interfaces: Normal form analysis of the Kuramoto–Sivashinsky equation
• Travelling-waves of the Kuramoto-Sivashinsky, equation: period-multiplying bifurcations
• Quasi-Elliptic Periodic Points in Conservative Dynamical Systems
• THE "COCOON" BIFURCATIONS IN THREE-DIMENSONAL SYSTEMS WITH TWO FIXED POINTS
• 𝐶¹ Connecting Lemmas
• Abundance of attracting, repelling and elliptic periodic orbits in two-dimensional reversible maps
• Abundance of elliptic isles at conservative bifurcations
• ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. II
• Rigorous verification of cocoon bifurcations in the Michelson system
• A pasting lemma and some applications for conservative systems
• The Lyapunov exponents of generic zero divergence three-dimensional vector fields
• Cocoon bifurcation in three-dimensional reversible vector fields
• On the Volume Elements on a Manifold
• ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. I
• On two-dimensional area-preserving diffeomorphisms with infinitely many elliptic islands

This page was built for publication: Dynamics of conservative Bykov cycles: tangencies, generalized Cocoon bifurcations and elliptic solutions