[HTML][HTML] New criteria for the monotonicity of the ratio of two Abelian integrals
C Liu, G Chen, Z Sun - Journal of Mathematical Analysis and Applications, 2018 - Elsevier
New criteria to determine the monotonicity of the ratio of two Abelian integrals are given.
When two Abelian integrals have the forms∫ Γ hf 1 (x) ydx and∫ Γ hf 2 (x) ydx or the …
When two Abelian integrals have the forms∫ Γ hf 1 (x) ydx and∫ Γ hf 2 (x) ydx or the …
[PDF][PDF] MONOTONICITY OF THE RATIOS OF TWO ABELIAN INTEGRALS FOR HAMILTONIAN SYSTEMS WITH PARAMETERS
Q Wang, N Wang, X Sun - Journal of Applied Analysis & …, 2024 - jaac-online.com
γi (h) ydx\∮ γi (h) xydx over three period annuli {γi (h)}, for i= 1, 2, 3, defined by a seventh-
degree hyperelliptic Hamiltonian H (x, y)= y2+ Ψ (x) with a parameter. The parameter makes …
degree hyperelliptic Hamiltonian H (x, y)= y2+ Ψ (x) with a parameter. The parameter makes …
Zeros of hyperelliptic integrals of the first kind for special hyperelliptic Hamiltonians of degree 7
A Bakhshalizadeh, R Asheghi, R Hoseyni - Chaos, Solitons & Fractals, 2017 - Elsevier
In this paper, we study the Chebyshev's property of the three-dimensional vector space E=<
J 0, J 1, J 2>, where J i (h)=∫ H= hxidxy and H (x, y)= 1 2 y 2+ V (x) is a hyperelliptic …
J 0, J 1, J 2>, where J i (h)=∫ H= hxidxy and H (x, y)= 1 2 y 2+ V (x) is a hyperelliptic …
[PDF][PDF] The number of zeros of Abelian integrals for a perturbation of a hyper-elliptic Hamiltonian system with a nilpotent center and a cuspidal loop
A Atabaigi - Electronic Journal of Qualitative Theory of Differential …, 2017 - real.mtak.hu
In this paper we consider the number of isolated zeros of Abelian integrals associated to the
perturbed system x= y, y=− x3 (x− 1) 2+ ε (α+ βx+ γx3) y, where ε> 0 is small and α, β, γ∈ R …
perturbed system x= y, y=− x3 (x− 1) 2+ ε (α+ βx+ γx3) y, where ε> 0 is small and α, β, γ∈ R …