Limit Cycles of Differential
نویسندگان
چکیده
vol. 37 (2008) No. 1 Book review: LIMIT CYCLES OF DIFFERENTIAL EQUATIONS by Colin Christopher and Chengzhi Li In June 2006 Jaume Llibre and Armengol Gasull organized the Advan ed Course on Limit Cy les and Di erential Equations at the Centre de Re er a Matemàti a in Bar elona. There were three le turers: two by the authors of this book and by Sergey Yakovenko. The book under review ontains the notes of le tures of Christopher and Li. (Yakovenko, worked hard, then, on his book on analyti di erential equations with Ilyashenko, whi h is now being published in AMS; so he did not prepare his notes for publi ation.) The book is divided into two parts: `Around the Center Fo us problem' by C. Christopher and `Abelian Integrals and Appli ations to the Weak Hilbert's 16th Problem' by C. Li. A singular point 0 of a real planar analyti ve tor eld V is alled the enter if there exists a neighborhood U of 0 su h that U \ 0 is lled with periodi integral urves of the eld. The problem of enter relies on nding onditions on the oe ients of the Taylor expansion of V at 0 whi h imply that 0 is a enter. Here we must distinguish lo al and global problems. The lo al problem of enter (or the enter fo us problem) was formulated by V. Arnold (1970) as follows: The spa e J of k−jets jV at 0 of germs
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