Limit Cycles of Differential Equations

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Beschreibung

This book contains the lecture series delivered at the "Advanced Course on Limit Cycles of Differential Equations." It covers the center-focus problem for polynomial vector fields and the application of abelian integrals to limit cycle bifurcations.

This textbook contains the lecture series originally delivered at the "Advanced Course on Limit Cycles of Differential Equations" in the Centre de Rechercha Mathematica Barcelona in 2006. It covers the center-focus problem for polynomial vector fields and the application of abelian integrals to limit cycle bifurcations. Both topics are related to the authors' interests in Hilbert's sixteenth problem, but would also be of interest to those working more generally in the qualitative theory of dynamical systems.

The book is well written and informative, including some recent references. It would be very useful as an introduction to the subject. (Iliya Iliev, zbMATH 1359.34001, 2017)



Klappentext

This textbook contains the lecture series originally delivered at the "Advanced Course on Limit Cycles of Differential Equations" in the Centre de Recerca Matemàtica Barcelona in 2006.

The topics covered are the center-focus problem for polynomial vector fields, and the application of abelian integrals to limit cycle bifurcations. Both topics are related to Hilbert's sixteenth problem. In particular, the book will be of interest to students and researchers working in the qualitative theory of dynamical systems.



Inhalt
Around the Center-Focus Problem.- Centers and Limit Cycles.- Darboux Integrability.- Liouvillian Integrability.- Symmetry.- Cherkas' Systems.- Monodromy.- The Tangential Center-Focus Problem.- Monodromy of Hyperelliptic Abelian Integrals.- Holonomy and the Lotka-Volterra System.- Other Approaches.- Abelian Integrals and Applications to the Weak Hilbert's 16th Problem.- Hilbert's 16th Problem and Its Weak Form.- Abelian Integrals and Limit Cycles.- Estimate of the Number of Zeros of Abelian Integrals.- A Unified Proof of the Weak Hilbert's 16th Problem for n=2.

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Produktinformationen

Titel
Limit Cycles of Differential Equations
Autor
EAN
9783764384098
ISBN
3764384093
Format
Kartonierter Einband
Genre
Mathematik
Anzahl Seiten
184
Gewicht
329g
Größe
H244mm x B170mm x T10mm
Jahr
2007
Untertitel
Englisch
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