Limit Cycles of Differential Equations / by Colin Christopher, Chengzhi Li, Joan Torregrosa.

Format:

Book

Author/Creator:

Christopher, Colin, author.

Li, Chengzhi, author.

Torregrosa, Joan, author.

Series:

Advanced Courses in Mathematics - CRM Barcelona, 2297-0312

Language:

English

Subjects (All):

Differential equations.

Dynamics.

Differential Equations.

Dynamical Systems.

Local Subjects:

Differential Equations.

Dynamical Systems.

Physical Description:

1 online resource (235 pages)

Edition:

2nd ed. 2024.

Place of Publication:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2024.

Summary:

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.

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.

Notes:

Includes bibliographical references.

Other Format:

Print version: Christopher, Colin Limit Cycles of Differential Equations

ISBN:

3-030-59656-7