Periodic solutions of nonlinear periodic differential systems with a small parameter

By Adriana Buica, Jean-Pierre Françoise, Jaume Llibre. 2006

160 citations recorded by the source corpus.

We deal with nonlinear periodic differential systems depending on a small parameter. The unperturbed system has an invariant manifold of periodic solutions. We provide sufficient conditions in order that some of the periodic orbits of this invariant manifold persist after the perturbation. These conditions are not difficult to check, as we show in some applications. The key tool for proving the main result is the Lyapunov--Schmidt reduction method applied to the Poincare--Andronov mapping.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/cd5be9343af19f461213662d41f6227d759871dc

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In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Averaging theory at any order for computing periodic orbits (2013, background): “The averaging theory of first order for studying periodic orbits of a differential equation (4) in Rn is very classical, see for instance Malkin [6], Roseau [7], Buică, Françoise and Llibre [2] where the authors studied the first order averaging theory of equations (7), and Buică, Giné and Llibre [3”
On the limit cycles of polynomial vector field (2011, background): “Theorem 5 goes back to Malkin [13] and Roseau [15], for a shorter proof see [2].”