Analytic and algebraic conditions for bifurcations of homoclinic orbits II: Reversible systems

DOI10.1007/s10884-021-10091-5zbMath1344.34054arXiv2107.12077WikidataQ115382957 ScholiaQ115382957MaRDI QIDQ2792103

Kazuyuki Yagasaki

Publication date: 16 March 2016

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

Full work available at URL: https://arxiv.org/abs/2107.12077

zbMATH Keywords

bifurcationhomoclinic orbithomoclinic orbitsdifferential Galois theoryMelnikov methodreversible system

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Bifurcation theory for ordinary differential equations (34C23) Averaging method for ordinary differential equations (34C29) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (4)

Analytic and algebraic conditions for bifurcations of homoclinic orbits II: Reversible systems ⋮ Integrability of the Zakharov-Shabat systems by quadrature ⋮ Bifurcations and spectral stability of solitary waves in coupled nonlinear Schrödinger equations ⋮ Bifurcations of radially symmetric solutions in a coupled elliptic system with critical growth in \(\mathbb{R}^d\) for \(d=3,4\)

Cites Work

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• Analytic and algebraic conditions for bifurcations of homoclinic orbits I: Saddle equilibria
• Time-reversal symmetry in dynamical systems: a survey
• Homoclinic period blow-up in reversible and conservative systems
• Bifurcation of degenerate homoclinic orbits in reversible and conservative systems
• Numerical computations for bifurcations and spectral stability of solitary waves in coupled nonlinear Schrödinger equations
• Bifurcations of radially symmetric solutions in a coupled elliptic system with critical growth in \(\mathbb{R}^d\) for \(d=3,4\)
• Detection of symmetric homoclinic orbits to saddle-centres in reversible systems
• Analytic and algebraic conditions for bifurcations of homoclinic orbits II: Reversible systems
• Picard-Vessiot Extensions of Real Differential Fields
• Homoclinic Solutions for Autonomous Dynamical Systems in Arbitrary Dimension
• Elements of applied bifurcation theory

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