Stability and uniqueness of periodic orbits produced during homoclinic bifurcation

DOI10.1007/BF02265392zbMath0839.34051OpenAlexW1992855210WikidataQ104208922 ScholiaQ104208922MaRDI QIDQ4860420

De-Ming Zhu

Publication date: 26 June 1996

Published in: Acta Mathematica Sinica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02265392

zbMATH Keywords

stabilitybifurcationperiodic orbithomoclinic orbit

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Asymptotic properties of solutions to ordinary differential equations (34D05) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (3)

Bifurcations and stability of nondegenerated homoclinic loops for higher dimensional systems ⋮ NONRESONANT BIFURCATIONS OF HETEROCLINIC LOOPS WITH ONE INCLINATION FLIP ⋮ Problems in homoclinic bifurcation with higher dimensions

Cites Work

• Homoclinic bifurcation at resonant eigenvalues
• The Sil'nikov problem, exponential expansion, strong \(\lambda\)-lemma, \(C^ 1\)-linearization, and homoclinic bifurcation
• Global bifurcations and chaos. Analytical methods
• Invariant manifolds
• Unnamed Item

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