Simple homoclinic cycles in low-dimensional spaces

DOI10.1016/j.jde.2004.10.023zbMath1066.34042OpenAlexW2028669236MaRDI QIDQ1763958

Nicola Sottocornola

Publication date: 22 February 2005

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

Full work available at URL: https://doi.org/10.1016/j.jde.2004.10.023

zbMATH Keywords

ordinary differential equationssystems with symmetryequivariant dynamical systemsrobust homoclinic cycles

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items

Pseudo-simple heteroclinic cycles in \(\mathbb{R}^4\), Stability of a heteroclinic network and its cycles: a case study from Boussinesq convection, Resonance bifurcation from homoclinic cycles, Simple heteroclinic networks in $ \newcommand{\R}{{{\mathbb R}}} \R^4$, Bifurcation from codimension one relative homoclinic cycles

Uses Software

• GAP

Cites Work

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• Symmetry breaking and branching patterns in equivariant bifurcation theory. II
• Transverse bifurcations of homoclinic cycles
• Robust heteroclinic cycles
• Complete classification of homoclinic cycles in \(\mathbb{R}^4\) in the case of a symmetry group \(G\subset\text{SO}(4)\).
• Rational products of sines of rational angles
• Some results on roots of unity, with an application to a diophantine problem
• Sur la classification des cycles homoclines dans
• Structural Stability of Equivariant Vector Fields on Two-Manifolds
• Structurally stable heteroclinic cycles
• Asymptotic stability of heteroclinic cycles in systems with symmetry
• Asymptotic stability of heteroclinic cycles in systems with symmetry. II
• Robust homoclinic cycles in  ⁴