Moduli for heteroclinic connections involving saddle-foci and periodic solutions

DOI10.3934/dcds.2015.35.3155zbMath1366.37052OpenAlexW2325760835MaRDI QIDQ255407

Alexandre A. P. Rodrigues

Publication date: 9 March 2016

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2015.35.3155

zbMATH Keywords

periodic solutionheteroclinic connectionsaddle-focusspinning in average

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Dynamics induced by flows and semiflows (37C10) Periodic orbits of vector fields and flows (37C27) Generic properties, structural stability of dynamical systems (37C20) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items (4)

Dynamics of conservative Bykov cycles: tangencies, generalized Cocoon bifurcations and elliptic solutions ⋮ Moduli of 3-dimensional diffeomorphisms with saddle-foci ⋮ Global bifurcations close to symmetry ⋮ Heteroclinic cycles and chaos in a class of 3D three-zone piecewise affine systems

Cites Work

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• Repelling dynamics near a Bykov cycle
• Global generic dynamics close to symmetry
• On Shilnikov's homoclinic-saddle-focus theorem
• Local and global behavior near homoclinic orbits
• The Sil'nikov problem, exponential expansion, strong \(\lambda\)-lemma, \(C^ 1\)-linearization, and homoclinic bifurcation
• Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. (On smooth conjugacy of diffeomorphisms of the circle with rotations)
• Possible new strange attractors with spiral structure
• A note on modulus of stability for cycles of the complex type
• Dynamical systems V. Bifurcation theory and catastrophe theory. Transl. from the Russian by N. D. Kazarinoff
• Elements of applied bifurcation theory.
• Bifurcations of systems with structurally unstable homoclinic orbits and moduli of \(\Omega\)-equivalence
• An existence criterion for conjugacy invariant of diffeomorphisms and vector fields
• Persistent switching near a heteroclinic model for the geodynamo problem
• Spiralling dynamics near heteroclinic networks
• Some topological invariants for three-dimensional flows
• Partial Symmetry Breaking and Heteroclinic Tangencies
• Chaotic double cycling
• Periodic attractors, strange attractors and hyperbolic dynamics near homoclinic orbits to saddle-focus equilibria
• Homoclinic Bifurcations in n Dimensions
• Switching near a network of rotating nodes
• ON SYSTEMS WITH A SADDLE-FOCUS HOMOCLINIC CURVE
• A modulus of 3-dimensional vector fields
• Time Averages for Heteroclinic Attractors
• Heteroclinic attractors: Time averages and moduli of topological conjugacy
• Asymptotic stability of heteroclinic cycles in systems with symmetry
• EXPONENTIAL EXPANSION WITH PRINCIPAL EIGENVALUES
• Équivalence topologique de connexions de selles en dimension 3
• Asymptotic stability of heteroclinic cycles in systems with symmetry. II
• SIMPLE VECTOR FIELDS WITH COMPLEX BEHAVIOR

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