The number of limit cycles of polynomial deformations of a Hamiltonian vector field

DOI10.1017/S0143385700005721zbMath0691.58031OpenAlexW2083803530MaRDI QIDQ3033029

Pavao Mardešić

Publication date: 1990

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385700005721

zbMATH Keywords

limit cyclesAbelian integrals

Mathematics Subject Classification ID

Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (16)

Unfolding of a quadratic integrable system with two centers and two unbounded heteroclinic loops ⋮ Double exponential estimate for the number of zeros of complete Abelian integrals and rational envelopes of linear ordinary differential equations with an irreducible monodromy group ⋮ Perturbations of quadratic centers ⋮ On the number of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems with one nilpotent saddle ⋮ On the limit cycles available from polynomial perturbations of the Bogdanov-Takens Hamiltonian ⋮ Bogdanov-Takens bifurcation in predator-prey systems ⋮ HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS ⋮ Perturbations of the non-generic quadratic Hamiltonian vector fields with hyperbolic segment ⋮ On Hopf cyclicity of planar systems with multiple parameters ⋮ On Uniqueness of Limit Cycles in General Bogdanov–Takens Bifurcation ⋮ Hopf and homoclinic bifurcations for near-Hamiltonian systems ⋮ On Hopf cyclicity of planar systems ⋮ Abelian integrals related to Morse polynomials and perturbations of plane Hamiltonian vector fields ⋮ Affine upper bounds for the number of zeros of abelian integrals for quartic elliptic Hamiltonians ⋮ Linear estimation of the number of zeros of abelian integral for some cubic isochronous centers ⋮ Bifurcation of a class of planar non-Hamiltonian integrable systems with one center and one homoclinic loop

Cites Work

• Number of zeros of complete elliptic integrals
• Estimate of the number of zeros of an Abelian integral depending on a parameter and limit cycles
• The Chebyshev property of elliptic integrals
• On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
• The multiplicity of limit cycles arising from perturbations of the form 𝑤’=𝑃₂/𝑄₁ of a Hamilton equation in the real and complex domain

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