Limit Cycles of Differential Equations
Springer Basel (Verlag)
978-3-7643-8409-8 (ISBN)
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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.
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.
"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)
| Erscheint lt. Verlag | 16.5.2007 |
|---|---|
| Reihe/Serie | Advanced Courses in Mathematics - CRM Barcelona |
| Zusatzinfo | VIII, 171 p. |
| Verlagsort | Basel |
| Sprache | englisch |
| Maße | 170 x 244 mm |
| Gewicht | 510 g |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Schlagworte | Abelian integral • Center-focus problem • differential equation • Differenzialgleichungen • Dynamical Systems • Hilbert's 16th problem • Limit cycle • Ordinary differential equations |
| ISBN-10 | 3-7643-8409-3 / 3764384093 |
| ISBN-13 | 978-3-7643-8409-8 / 9783764384098 |
| Zustand | Neuware |
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