Melnikov method for perturbed completely integrable systems
Copyright policy )Melnikov method for perturbed completely integrable systems
We consider a completely integrable system of differential equations in arbitrary dimensions whose phase space contains an open set foliated by periodic orbits. This research analyzes the persistence and stability of the periodic orbits under a nonlinear periodic perturbation. For this purpose, we use the Melnikov method and Floquet theory to establish conditions for the existence and stability of periodic orbits. Our approach considers periods of the unperturbed orbits depending on the integrals and constant periods. In the applications, we deal with both cases. Precisely, we study the existence of periodic orbits in a perturbed generalized Euler system. In the degenerate case, we analyze the existence and stability of periodic orbits for a perturbed harmonic oscillator.
completely integrable systems, Perturbations, asymptotics of solutions to ordinary differential equations, Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.), Nonautonomous smooth dynamical systems, FOS: Mathematics, Melnikov method, Dynamical Systems (math.DS), Stability of solutions to ordinary differential equations, Mathematics - Dynamical Systems, Periodic solutions to ordinary differential equations, periodic orbits
completely integrable systems, Perturbations, asymptotics of solutions to ordinary differential equations, Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.), Nonautonomous smooth dynamical systems, FOS: Mathematics, Melnikov method, Dynamical Systems (math.DS), Stability of solutions to ordinary differential equations, Mathematics - Dynamical Systems, Periodic solutions to ordinary differential equations, periodic orbits
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