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Theory of Limit Cycles

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Yan-Qian Ye and Chi Y Lo. Translated by Chi Y. Lo

Publication: Translations of Mathematical Monographs
Publication Year: 1986; Volume 66
ISBNs: 978-0-8218-4773-2 (print); 978-1-4704-4480-8 (online)
DOI: https://doi.org/10.1090/mmono/066
MathSciNet review: MR854278
MSC: Primary 58F21; Secondary 34C05

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Table of Contents

Front/Back Matter

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Chapters

• Introduction
• Fundamental Concepts, Concrete Examples, and Several Criteria to Establish Existence and Nonexistence of Limit Cycles
• Multiplicity and Stability of Limit Cycles
• Limit Cycles in Rotated Vector Fields
• General Behavior of Limit Cycles Depending on a Parameter
• Existence of a Limit Cycle
• Uniqueness of a Limit Cycle
• Existence of Several Limit Cycles
• Structural Stability of Differential Systems
• Work of M. Frommer and N. N. Bautin
• Global Structural Analysis of Some Quadratic Systems without Limit Cycles
• General Properties and Relative Positions of Limit Cycles in Quadratic Differential Systems
• Classification of Quadratic Differential Systems. Limit Cycles of Equations of Class I
• Global Structure of Trajectories of Equations of Class II without Limit Cycles
• Relative Positions of Limit Cycles and Conditions for Having at Most One and Two Limit Cycles in Equations of Class II
• Some Local and Global Properties of Equations of Class III
• The Method of Dulac Functions in the Qualitative Study of Quadratic Systems
• Limit Cycles in Bounded Quadratic Systems
• Appendix

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