Bifurcation of degenerate homoclinic orbits to saddle-center in reversible systems

DOI10.1007/s11401-008-0038-5zbMath1197.34067OpenAlexW2171990782MaRDI QIDQ1044778

De-Ming Zhu, Xing Bo Liu

Publication date: 15 December 2009

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11401-008-0038-5

zbMATH Keywords

bifurcationhomoclinic orbitsreversible systemsaddle-center

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Bifurcation theory for ordinary differential equations (34C23) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Bifurcations connected with nontransversal intersection in dynamical systems (37G25)

Related Items (2)

The twisting bifurcations of double homoclinic loops with resonant eigenvalues ⋮ Existence of canards under non-generic conditions

Cites Work

• Unnamed Item
• Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics
• Global bifurcations and chaos. Analytical methods
• Homoclinic period blow-up in reversible and conservative systems
• When gap solitons become embedded solitons: A generic unfolding
• Detection of symmetric homoclinic orbits to saddle-centres in reversible systems
• Bifurcation of Homoclinic Orbits to a Saddle-Center in Reversible Systems
• Using Melnikov's method to solve Silnikov's problems
• Embedded solitons: Solitary waves in resonance with the linear spectrum

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