Improving the averaging theory for computing periodic solutions of the differential equations

DOI10.1007/s00033-014-0460-3zbMath1359.37109OpenAlexW2027016366MaRDI QIDQ493547

Jaume Llibre, Douglas Duarte Novaes

Publication date: 3 September 2015

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/150685

zbMATH Keywords

periodic solutionslimit cyclesLyapunov-Schmidt reductionaveraging theorynonlinear differential systems

Mathematics Subject Classification ID

Averaging method for ordinary differential equations (34C29) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Related Items (15)

Limit Cycles of a Class of Discontinuous Piecewise Differential Systems Separated by the Curve y = xn Via Averaging Theory ⋮ Piecewise smooth dynamical systems: persistence of periodic solutions and normal forms ⋮ Affine-periodic solutions by asymptotic method ⋮ Limit cycles of piecewise polynomial perturbations of higher dimensional linear differential systems ⋮ New symmetric periodic solutions for the Maxwell-Bloch differential system ⋮ Persistence of periodic solutions for higher order perturbed differential systems via Lyapunov–Schmidt reduction ⋮ An abstract averaging method with applications to differential equations ⋮ Averaging methods for nonlinear systems with a small parameter via reduction and topological degree ⋮ Stability of Periodic Orbits in the Averaging Theory: Applications to Lorenz and Thomas Differential Systems ⋮ Affine-periodic solutions by averaging methods ⋮ New results on averaging theory and applications ⋮ Zero-Hopf bifurcations in 3-dimensional differential systems with no equilibria ⋮ Homoclinic, heteroclinic and periodic orbits of singularly perturbed systems ⋮ On the existence of periodic orbits and KAM tori in the Sprott A system: a special case of the Nosé-Hoover oscillator ⋮ Bifurcations from families of periodic solutions in piecewise differential systems

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