Averaging theory at any order for computing periodic orbits

By Jaume Giné Mesa, Maite Grau, Jaume Llibre. 2013

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Abstract We provide a recurrence formula for the coefficients of the powers of e in the series expansion of the solutions around e = 0 of the perturbed first-order differential equations. Using it, we give an averaging theory at any order in e for the following two kinds of analytic differential equation: d x d θ = ∑ k ≥ 1 e k F k ( θ , x ) , d x d θ = ∑ k ≥ 0 e k F k ( θ , x ) . A planar polynomial differential system with a singular point at the origin can be transformed, using polar coordinates, to an equation of the previous form. Thus, we apply our results for studying the limit cycles of a planar polynomial differential systems.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f61d1f5b98d63da310933fd9d3a89f86e722fd3b