Limit Cycles of Differential Equations

This textbook covers the center-focus problem for polynomial vector fields and the application of abelian integrals to limit cycle bifurcations, both topics related to Hilbert's sixteenth problem.

Format: Paperback / softback
Length: 238 pages
Publication date: 23 January 2024
Publisher: Springer Nature Switzerland AG

This comprehensive textbook serves as a valuable resource for those seeking to delve into the intricate world of Limit Cycles of Differential Equations. Originally presented as a lecture series during the Advanced Course on Limit Cycles of Differential Equations held at the Centre de Rechercha Mathematica Barcelona in 2006, it offers a comprehensive exploration of two key topics: the center-focus problem for polynomial vector fields and the application of abelian integrals to limit cycle bifurcations. While these subjects may initially seem closely related to the author's personal interests in Hilbert's sixteenth problem, they hold immense significance for researchers and scholars engaged in the broader field of qualitative theory of dynamical systems.

The center-focus problem, a fundamental aspect of the study of Limit Cycles, involves analyzing the behavior of polynomial vector fields when they are subjected to certain constraints. By studying the properties of these fields, researchers can gain insights into the formation and stability of limit cycles, which are important phenomena in dynamical systems. The application of abelian integrals to limit cycle bifurcations is another crucial aspect covered in this textbook. Abelian integrals are mathematical tools that are used to compute the growth rates of functions, and they play a vital role in understanding the dynamics of complex systems. By analyzing the behavior of abelian integrals, researchers can identify critical points where limit cycles may bifurcate, leading to the emergence of new stable states or chaotic behavior.

The authors of this textbook have done an exceptional job in presenting the material in a clear and concise manner, making it accessible to a wide range of readers. The chapters are well-organized, and each section is accompanied by detailed examples and exercises to help reinforce the concepts discussed. Additionally, the book includes a comprehensive bibliography that provides further reading for those who wish to explore these topics in greater depth. Whether you are a student, researcher, or professional in the field of mathematics, this textbook is an invaluable resource that will enhance your understanding of Limit Cycles of Differential Equations and their applications.

In conclusion, this textbook is a must-read for anyone interested in the study of Limit Cycles of Differential Equations. Its comprehensive coverage of the center-focus problem and the application of abelian integrals to limit cycle bifurcations makes it an essential resource for researchers and scholars in the field. With its clear and concise presentation, detailed examples, and comprehensive bibliography, this book is sure to deepen your understanding of these complex topics and inspire your future research endeavors.

Weight: 426g
Dimension: 240 x 168 (mm)
ISBN-13: 9783030596552
Edition number: 2nd ed. 2024