Global generic dynamics close to symmetry

DOI10.1016/j.jde.2012.06.009zbMath1255.34045OpenAlexW1973887680MaRDI QIDQ449253

Alexandre A. P. Rodrigues, Isabel Salgado Labouriau

Publication date: 12 September 2012

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

Full work available at URL: https://doi.org/10.1016/j.jde.2012.06.009

zbMATH Keywords

symmetry breakingBykov cyclesheteroclinic networksShilnikov's homoclinic cycles

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Symmetries, invariants of ordinary differential equations (34C14) Bifurcation theory for ordinary differential equations (34C23) Perturbations of ordinary differential equations (34D10) Averaging method for ordinary differential equations (34C29) Complex behavior and chaotic systems of ordinary differential equations (34C28) Dynamical systems with hyperbolic orbits and sets (37D05) Dynamical aspects of attractors and their bifurcations (37G35) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items

Dynamics of conservative Bykov cycles: tangencies, generalized Cocoon bifurcations and elliptic solutions, Large strange attractors in the unfolding of a heteroclinic attractor, Unfolding a Bykov attractor: from an attracting torus to strange attractors, On the Dynamics Near a Homoclinic Network to a Bifocus: Switching and Horseshoes, Repelling dynamics near a Bykov cycle, Using Lin's method to solve Bykov's problems, Abundance of Infinite Switching, Experimentally Accessible Orbits Near a Bykov Cycle, Spiralling dynamics near heteroclinic networks, Dense heteroclinic tangencies near a Bykov cycle, Attractors in complex networks, Global bifurcations close to symmetry, Torus-Breakdown Near a Heteroclinic Attractor: A Case Study, Switching in Heteroclinic Networks, The role of the saddle-foci on the structure of a Bykov attracting set, Shift dynamics near non-elementary T-points with real eigenvalues, Moduli for heteroclinic connections involving saddle-foci and periodic solutions, Infinitely many multi-pulses near a bifocal cycle

Cites Work

• Intermittency as a codimension-three phenomenon
• Shil'nikov configurations in any generic unfolding of the nilpotent singularity of codimension three on \(\mathbb R^3\)
• Period doubling cascades of attractors: A prerequisite for horseshoes
• Local and global behavior near homoclinic orbits
• T-points: A codimension two heteroclinic bifurcation
• Global bifurcations and chaos. Analytical methods
• Coexistence of the chaos and the periodic solutions in planar fluid flows
• Abundance of strange attractors
• On the \(C^{1}\) normal forms for hyperbolic vector fields
• T-points in a \(\mathbb Z_2\)-symmetric electronic oscillator. I: Analysis
• Accumulations of \(T\)-points in a model for solitary pulses in an excitable reaction-diffusion medium
• Determination of generalized horseshoe maps inducing all link types
• Forced symmetry breaking of homoclinic cycles in a PDE with O(2) symmetry
• Heteroclinic bifurcations near Hopf-zero bifurcation in reversible vector fields in \(\mathbb R^3\)
• Chaotic double cycling
• Switching homoclinic networks
• The effect of symmetry breaking on the dynamics near a structurally stable heteroclinic cycle between equilibria and a periodic orbit
• Switching near a network of rotating nodes
• Existence of a Reversible T-Point Heteroclinic Cycle in a Piecewise Linear Version of the Michelson System
• Entropy and Knots
• Asymptotic stability of heteroclinic cycles in systems with symmetry
• Parameter dependence of homoclinic solutions in a single long Josephson junction
• THE THIRD POWER OF THE SMALE HORSESHOE INDUCES ALL LINK TYPES
• Dynamics near a heteroclinic network
• SIMPLE VECTOR FIELDS WITH COMPLEX BEHAVIOR
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item