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Integrability and limit cycles for Abel equations. (English) Zbl 1248.34031

Crespo, Teresa (ed.) et al., Algebraic methods in dynamical systems. Proceedings of the conference, Będlewo, Poland, May 16–22, 2010. Dedicated to Michael Singer on his 60th birthday. Warszawa: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-13-3/pbk). Banach Center Publications 94, 187-196 (2011).
The paper contains some results concerning integrability and limit cycles for polynomial Abel equations \[ \frac{dy}{dx}=p(x)y^2+q(x)y^3. \] It is proved that Abel equations have a Godbillon-Vey sequence of length \(4\). The author shows that the associated Poincaré mapping can be expressed by iterated integrals with three functions which are solutions of a system of partial differential equations.
For the entire collection see [Zbl 1230.00043].

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34A05 Explicit solutions, first integrals of ordinary differential equations
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