Cover Image

Limit Cycles of Differential Equations

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 abel...

Full description

Main Authors: Christopher, Colin. (Author, http://id.loc.gov/vocabulary/relators/aut), Li, Chengzhi. (http://id.loc.gov/vocabulary/relators/aut)
Corporate Author: SpringerLink (Online service)
Language:English
Published: Basel : Birkhäuser Basel : Imprint: Birkhäuser, 2007.
Edition:1st ed. 2007.
Series:Advanced Courses in Mathematics - CRM Barcelona,
Subjects:
Differential equations.
Dynamics.
Ergodic theory.
Ordinary Differential Equations.
Dynamical Systems and Ergodic Theory.
Online Access:https://doi.org/10.1007/978-3-7643-8410-4
Table of Contents:
  • 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.

Similar Items