Non-oscillation of elliptic integrals

DOI10.1007/BF01077961zbMath0738.33013OpenAlexW2052159825MaRDI QIDQ1813418

G. S. Petrov

Publication date: 25 June 1992

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01077961

zbMATH Keywords

elliptic integral

Mathematics Subject Classification ID

Algebraic theory of abelian varieties (14K05) Elliptic functions and integrals (33E05)

Related Items (30)

Tangential Hilbert problem for perturbations of hyperelliptic Hamiltonian systems ⋮ Estimate of the number of zeros of abelian integrals for a kind of quartic Hamiltonians with two centers ⋮ Cubic perturbations of elliptic Hamiltonian vector fields of degree three ⋮ On the number of limit cycles in perturbations of a two dimensional nonlinear differential system ⋮ On the classification of elliptic foliations induced by real quadratic fields with center ⋮ Simple exponential estimate for the number of real zeros of complete abelian integrals ⋮ Perturbations of quadratic Hamiltonian systems with symmetry ⋮ Analysis and synthesis of oscillator systems described by a perturbed double-well Duffing equation ⋮ On the number of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems with one nilpotent saddle ⋮ Cyclicity of a Family of Generic Reversible Quadratic Systems with One Center ⋮ Perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain ⋮ Linear estimate of the number of limit cycles for a class of nonlinear systems ⋮ On the number of zeros of Abelian integrals for a polynomial Hamiltonian irregular at infinity ⋮ Analysis and synthesis of oscillator systems described by perturbed single well Duffing equations ⋮ The period function for quadratic integrable systems with cubic orbits ⋮ Linear estimate on the number of zeros of Abelian integrals for quadratic centers having almost all their orbits formed by cubics ⋮ Perturbations from an elliptic Hamiltonian of degree four. I: Saddle loop and two saddle cycles ⋮ Complete hyperelliptic integrals of the first kind and their non-oscillation ⋮ Limit cycles bifurcating from the period annulus of quasi-homogeneous centers ⋮ Quadratic perturbations of quadratic codimension-four centers ⋮ Petrov modules and zeros of abelian integrals ⋮ Abelian integrals related to Morse polynomials and perturbations of plane Hamiltonian vector fields ⋮ THE NUMBER OF ZEROS OF ABELIAN INTEGRALS FOR A PERTURBATION OF HYPERELLIPTIC HAMILTONIAN SYSTEM WITH DEGENERATED POLYCYCLE ⋮ Linear estimate of the number of zeros of Abelian integrals for a kind of quartic Hamiltonians ⋮ The monotonicity of the ratio of two Abelian integrals ⋮ Affine upper bounds for the number of zeros of abelian integrals for quartic elliptic Hamiltonians ⋮ Cubic perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain ⋮ Linear estimation of the number of zeros of abelian integral for some cubic isochronous centers ⋮ Perturbations of quadratic Hamiltonian two-saddle cycles ⋮ Perturbation from an elliptic Hamiltonian of degree four. IV: Figure eight-loop.

Cites Work

• Invariant elements in modular lattices
• Reduction to orbital normal form of a vector field on the plane
• Genus \(\chi_y\) of quasihomogeneous complete intersections
• On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
• Complex zeros of an elliptic integral

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