Expansion Coefficients and Their Relation for Melnikov Functions Near Polycycles
Copyright policy )Expansion Coefficients and Their Relation for Melnikov Functions Near Polycycles
Assuming a particular condition, the authors present novel results concerning expansion coefficients and their interrelation within the first-order Melnikov functions. These results, derived for m-polycycles (where m is a positive integer) with hyperbolic saddles, lead to a comprehensive bifurcation theory for predicting limit cycles near these polycycles. This allows us to precisely count the limit cycles appearing close to the polycycle containing two hyperbolic saddles. The results will very helpful to consider polycyclic bifurcations.
- Zhejiang Normal University China (People's Republic of)
- Fuyang Normal University China (People's Republic of)
Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion, Bifurcation theory for ordinary differential equations, limit cycle, Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.), Melnikov function, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Homoclinic and heteroclinic solutions to ordinary differential equations, polycycle
Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion, Bifurcation theory for ordinary differential equations, limit cycle, Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.), Melnikov function, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Homoclinic and heteroclinic solutions to ordinary differential equations, polycycle
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