Limit Cycles of Differential Equations
Series: Advanced Courses in Mathematics - CRM Barcelona;
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Product details:
- Edition number 2nd ed. 2024
- Publisher Birkhäuser
- Date of Publication 23 January 2024
- Number of Volumes 1 pieces, Book
- ISBN 9783030596552
- Binding Paperback
- No. of pages238 pages
- Size 240x168 mm
- Weight 426 g
- Language English
- Illustrations 16 Illustrations, black & white; 5 Illustrations, color 573
Categories
Short description:
This textbook contains the lecture series originally delivered at the "Advanced Course on Limit Cycles of Differential Equations" in the Centre de Recerca Matem?tica 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.
This second edition provides updates, further clarifications and remarks, and includes an expanded list of references.
Long description:
This textbook contains the lecture series originally delivered at the "Advanced Course on Limit Cycles of Differential Equations" in the Centre de Recerca Matem?tica 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.This second edition provides updates, further clarifications and remarks, and includes an expanded list of references.
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Table of Contents:
Part I: Around the Center-Focus Problem.- 1 Centers and Limit Cycles.- 2 Darboux Integrability.- 3 Liouvillian Integrability.- 4 Symmetry.- 5 Cherkas? Systems.- 6 Monodromy.- 7 The Tangential Center-Focus Problem.- 8 Monodromy of Hyperelliptic Abelian Integrals.- 9 Holonomy and the Lotka-Volterra System.- 10 Other Approaches.- Part II: Abelian Integrals and Applications to the Weak Hilbert?s 16th Problem.- 1 Hilbert?s 16th Problem and Its Weak Form.- 2 Abelian Integrals and Limit Cycles.- 3 Estimate of the Number of Zeros of Abelian Integrals.- 4 A Unified Proof of the Weak Hilbert?s 16th Problem for n=2.
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Limit Cycles of Differential Equations
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