Upper Bound on the Number of Zeros of Abelian Integrals for Hyperbolic Hamiltonian Systems of Degree Seven
DOI10.1142/S0218127422500870zbMath1506.37078WikidataQ114072975 ScholiaQ114072975MaRDI QIDQ5083107
No author found.
Publication date: 21 June 2022
Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)
upper boundlimit cyclenumber of zerosheteroclinic loopabelian integralextended complete Chebyshev system
Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems (37J20) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46) Relations of finite-dimensional Hamiltonian and Lagrangian systems with algebraic geometry, complex analysis, special functions (37J38)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Bifurcation of limit cycles from a heteroclinic loop with a cusp
- Bounding the number of zeros of certain abelian integrals
- Normal forms, Melnikov functions and bifurcations of limit cycles
- A unified proof of the weakened Hilbert 16th problem for \(n=2\)
- On Melnikov functions of a homoclinic loop through a nilpotent saddle for planar near-Hamiltonian systems
- Limit cycles near homoclinic and heteroclinic loops
- Mathematical problems for the next century
- Perturbation of a period annulus bounded by a heteroclinic loop connecting two hyperbolic saddles
- Perturbations of a class of hyper-elliptic Hamiltonian systems of degree seven with nilpotent singular points
- Perturbation from an elliptic Hamiltonian of degree four. III: global centre.
- Perturbation from an elliptic Hamiltonian of degree four. IV: Figure eight-loop.
- Parameter identification on abelian integrals to achieve Chebyshev property
- Cyclicity of periodic annulus and Hopf cyclicity in perturbing a hyper-elliptic Hamiltonian system with a degenerate heteroclinic loop
- Exact bound on the number of zeros of abelian integrals for two hyper-elliptic Hamiltonian systems of degree 4
- Perturbation of a period annulus bounded by a saddle-saddle cycle in a hyperelliptic Hamiltonian systems of degree seven
- Perturbation of a period annulus with a unique two-saddle cycle in higher order Hamiltonian
- Limit cycle bifurcations by perturbing a cuspidal loop in a Hamiltonian system
- Bifurcation of limit cycles from a Liénard system with a heteroclinic loop connecting two nilpotent saddles
- A Chebyshev criterion for Abelian integrals
- Limit cycles of the generalized polynomial Liénard differential equations
- LIMIT CYCLE BIFURCATIONS NEAR A DOUBLE HOMOCLINIC LOOP WITH A NILPOTENT SADDLE
- ASYMPTOTIC EXPANSIONS OF MELNIKOV FUNCTIONS AND LIMIT CYCLE BIFURCATIONS
- EXACT BOUND ON THE NUMBER OF LIMIT CYCLES ARISING FROM A PERIODIC ANNULUS BOUNDED BY A SYMMETRIC HETEROCLINIC LOOP
- Strongly nonlinear oscillators. Analytical solutions
- Perturbations from an elliptic Hamiltonian of degree four. II: Cuspidal loop
- Perturbations from an elliptic Hamiltonian of degree four. I: Saddle loop and two saddle cycles
This page was built for publication: Upper Bound on the Number of Zeros of Abelian Integrals for Hyperbolic Hamiltonian Systems of Degree Seven
