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Periodic solutions of second-order differential equations with two-dimensional Lie point symmetry algebra

✍ Scribed by Isaac A. García; Jaume Giné; Susanna Maza

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
426 KB
Volume
11
Category
Article
ISSN
1468-1218

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✦ Synopsis

In this paper, we study some aspects of the dynamics in the phase plane of smooth secondorder differential equations ẍ = w(x, ẋ) possessing an r-dimensional Lie point symmetry algebra L r with r ≥ 2, focusing on the existence, nonexistence and localization periodic orbits. Finally, it is proved that the polynomial Liénard systems ẍ = f (x)ẋ + g(x) with f , g ∈ R[x] having an L r with r ≥ 2 do not have limit cycles. As far as we know, this is the first work that relates Lie point symmetries and periodic orbits.

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