Studying the upper bounds of the numbers of zeros of abelian integrals by the law of polynomials
DOI10.1142/S0218127424500810zbMATH Open1546.34053MaRDI QIDQ6608833
Xiaochun Hong, Lijun Hong, Jinling Liu
Publication date: 20 September 2024
Published in: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering (Search for Journal in Brave)
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)
Cites Work
- Title not available (Why is that?)
- Hopf and homoclinic bifurcations for near-Hamiltonian systems
- Perturbations of quadratic centers of genus one
- Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields
- On the Chebyshev property of certain abelian integrals near a polycycle
- Linear estimate for the number of zeros of abelian integrals
- The cyclicity of quadratic reversible systems with a center of genus one and non-Morsean point
- The perturbation of a class of hyper-elliptic Hamilton system with a double eight figure loop
- The smallest upper bound on the number of zeros of abelian integrals
- Number of zeros of complete abelian integrals for a primitive rational polynomial with non-trivial global monodromy
- Darboux systems with a cusp point and pseudo-abelian integrals
- On the abelian integrals of quadratic reversible centers with orbits formed by genus one curves of higher degree
- On the bifurcation of limit cycles due to polynomial perturbations of Hamiltonian centers
- The cyclicity of period annuli of a class of quintic Hamiltonian systems
- Linear estimate on the number of zeros of Abelian integrals for quadratic centers having almost all their orbits formed by cubics
- Estimating the number of zeros for Abelian integrals of quadratic reversible centers with orbits formed by higher-order curves
- Abelian integrals for quadratic centres having almost all their orbits formed by quartics*
- Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians
- The number of zeros of Abelian integrals for a perturbation of a hyper-elliptic Hamiltonian system with a nilpotent center and a cuspidal loop
- Bifurcation of Limit Cycles from a Class of Piecewise Smooth Systems with Two Vertical Straight Lines of Singularity
- HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
- Bifurcations of limit cycles from quadratic non-Hamiltonian systems with two centres and two unbounded heteroclinic loops
- A LINEAR ESTIMATION TO THE NUMBER OF ZEROS FOR ABELIAN INTEGRALS IN A KIND OF QUADRATIC REVERSIBLE CENTERS OF GENUS ONE
- UPPER BOUNDS FOR THE ASSOCIATED NUMBER OF ZEROS OF ABELIAN INTEGRALS FOR TWO CLASSES OF QUADRATIC REVERSIBLE CENTERS OF GENUS ONE
- LIMIT CYCLES FOR TWO CLASSES OF PLANAR POLYNOMIAL DIFFERENTIAL SYSTEMS WITH UNIFORM ISOCHRONOUS CENTERS
- Limit Cycles of Differential Equations
- Abelian integrals for a kind of quadratic reversible centers of genus one \((r7)\)
This page was built for publication: Studying the upper bounds of the numbers of zeros of abelian integrals by the law of polynomials
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6608833)
