On the limit cycles available from polynomial perturbations of the Bogdanov-Takens Hamiltonian
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Publication:1972834
DOI10.1007/BF02810590zbMath0945.34020MaRDI QIDQ1972834
Publication date: 26 April 2000
Published in: Israel Journal of Mathematics (Search for Journal in Brave)
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)
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Cites Work
- Unnamed Item
- Unnamed Item
- Elliptic integrals and their nonoscillation
- Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields
- The first derivative of the period function of a plane vector field
- A note on a result of G. S. Petrov about the weakened 16th Hilbert problem
- Higher-order Melnikov functions for degenerate cubic Hamiltonians
- The number of limit cycles of polynomial deformations of a Hamiltonian vector field
- On Second Order Bifurcations of Limit Cycles
- Successive derivatives of a first return map, application to the study of quadratic vector fields