Dynamics and geometry near resonant bifurcations

DOI10.1134/S1560354710520023zbMath1218.37064OpenAlexW2042346613WikidataQ58117844 ScholiaQ58117844MaRDI QIDQ2430534

S. J. Holtman, Renato Vitolo, Henk W. Broer, Gert Vegter

Publication date: 7 April 2011

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1560354710520023

zbMATH Keywords

Lyapunov-Schmidt reductiongeometric structureequivariant singularity theoryperiodically forced oscillatorresonant Hopf-Neimarck-Sacker bifurcation

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Averaging method for ordinary differential equations (34C29) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (3)

Resonance and fractal geometry ⋮ Quasi-periodic bifurcations of invariant circles in low-dimensional dissipative dynamical systems ⋮ Resonance and Singularities

Cites Work

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• Recognition of the bifurcation type of resonance in mildly degenerate Hopf–Neĭmark–Sacker families
• The geometry of resonance tongues: a singularity theory approach
• Elements of applied bifurcation theory

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