On the periodic solutions of a linear chain of three identical atoms

On the periodic orbits of the perturbed Wilberforce pendulum

“…For doing this we shall use the averaging theory of dynamical systems (see the Appendix for more details). We have been inspired by other works where these techniques have been used for studying other perturbed dynamical problems; see for instance Basu and Gewei (2011), Bustos et al (2013), Bustos et al (2014), Gao et al (2013), Guirao et al (2013a), and Guirao et al (2013b).…”

The Circular Hill Problem Regarding Arbitrary Disturbing Forces: The Periodic Solutions that are Emerging from the Equilibria

“…In Section 2, Theorem 1 will be proved using the averaging theory (see [13][14][15][16][17][18]). In the next corollary, an application of Theorem 1 is shown, whose proof is implemented in Section 3.…”

Periodic solutions of nonlinear differential systems by the method of averaging

“…Both classical averaging theorem [24] and local averaging theorem [4] proposed by Buicȃ, Françoise, and Llibre have been applied widely for various fields, see e.g. [16], [18], [23], [6], [5], [17]. There are a lot of papers on the local averaging theorem, see [20], [13], [21].…”