THE ABELIAN INTEGRALS OF A ONE-PARAMETER HAMILTONIAN SYSTEM UNDER POLYNOMIAL PERTURBATIONS
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Publication:4658999
DOI10.1142/S0218127404010692zbMath1070.34051OpenAlexW4241084471MaRDI QIDQ4658999
Wencheng Chen, Tonghua Zhang, Hong Zang, Mao'an Han
Publication date: 21 March 2005
Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1142/s0218127404010692
Periodic solutions to ordinary differential equations (34C25) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)
Related Items (5)
ABELIAN INTEGRALS FOR THE ONE-PARAMETER BOGDANOV–TAKENS SYSTEM ⋮ Bifurcation theory for finitely smooth planar autonomous differential systems ⋮ Perturbation of a period annulus bounded by a heteroclinic loop connecting two hyperbolic saddles ⋮ Limit cycle bifurcations in a class of near-Hamiltonian systems with multiple parameters ⋮ Analysis on bifurcations of multiple limit cycles for a parametrically and externally excited mechanical system
Cites Work
- Estimate of the number of zeros of an Abelian integral depending on a parameter and limit cycles
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- Cyclicity of planar homoclinic loops and quadratic integrable systems
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- On the number of limit cycles in double homoclinic bifurcations
- A note on a result of G. S. Petrov about the weakened 16th Hilbert problem
- Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians
- Nonoscillation of Elliptic Integrals Related to Cubic Polynomials with Symmetry of Order Three
- On Second Order Bifurcations of Limit Cycles
- Existence of at most 1, 2, or 3 zeros of a Melnikov function and limit cycles
- On the limit cycles of planar autonomous systems
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