Limit Cycles of Differential Equations - Colin Christopher, Chengzhi Li, Joan Torregrosa

Limit Cycles of Differential Equations

Buch | Softcover
IX, 238 Seiten
2024 | 2nd ed. 2024
Springer International Publishing (Verlag)
978-3-030-59655-2 (ISBN)
26,74 inkl. MwSt

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.

This second edition provides updates, further clarifications and remarks, and includes an expanded list of references.


Colin Christopher is Associate Head of School at the University of Plymouth in Devon, UK.

Chengzhi Li is Professor Emeritus at the Peking University in China.

Joan Torregrosa is Associate Professor at the Universitat Autònoma de Barcelona in Bellaterra, Spain.

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.

Erscheinungsdatum
Reihe/Serie Advanced Courses in Mathematics - CRM Barcelona
Zusatzinfo IX, 238 p. 21 illus., 5 illus. in color.
Verlagsort Cham
Sprache englisch
Maße 168 x 240 mm
Gewicht 426 g
Themenwelt Mathematik / Informatik Informatik Theorie / Studium
Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Technik Maschinenbau
Schlagworte Abelian integral • Center-focus problem • differential equation • Dynamical Systems • Hilbert's 16th problem • Limit cycle
ISBN-10 3-030-59655-9 / 3030596559
ISBN-13 978-3-030-59655-2 / 9783030596552
Zustand Neuware
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