The Center and Focus Problem: Algebraic Solutions and Hypotheses

The Center and Focus Problem: Algebraic Solutions and Hypotheses, by M. N. Popa and V.V. Pricop, ISBN: 978-1-032-01725-9 (Hardback), focuses on an old problem of the qualitative theory of differential equations, called the Center and Focus Problem. It is intended for mathematicians, researchers, professors, and Ph.D. students working in differential equations, Lie algebras, commutative graded algebras, generating functions, and Hilbert series. A significant result is obtained in solving Poincaré's problem, which provides upper estimations of the number of Poincaré-Lyapunov quantities that are algebraically independent and participate in solving the Center and Focus Problem. These estimations are equal to Krull dimensions of Sibirsky graded algebras of comitants and invariants of systems of differential equations.

Format: Hardback
Length: 210 pages
Publication date: 24 September 2021
Publisher: Taylor & Francis Ltd

This captivating book delves into an ancient problem within the realm of qualitative theory of differential equations, known as the Center and Focus Problem. Its intended audience encompasses mathematicians, researchers, professors, and Ph.D. students actively engaged in the study of differential equations, as well as other experts intrigued by the theories of Lie algebras, commutative graded algebras, generating functions, and Hilbert series. The book showcases the authors' remarkable achievements over the past decades.

One of the significant outcomes achieved in this book is the solution of Poincaré's problem. Specifically, the authors present upper estimations of the number of Poincaré-Lyapunov quantities that are algebraically independent and play a crucial role in resolving the Center and Focus Problem. These estimations are equivalent to the Krull dimensions of Sibirsky graded algebras of comitants and invariants of systems of differential equations.

The book is organized into five chapters, each providing a comprehensive exploration of the topic. Chapter 1 introduces the problem and highlights its historical significance. Chapter 2 provides a comprehensive review of the existing literature on the Center and Focus Problem, while Chapter 3 presents the authors' original contributions. Chapters 4 and 5 explore further developments and applications of the results obtained.

Throughout the book, the authors employ a clear and concise writing style, making the content accessible to a wide range of readers. They include numerous examples and exercises to assist in understanding the concepts and applications discussed. Additionally, the book features an extensive bibliography that provides valuable references for further research.

In conclusion, "The Center and Focus Problem: Algebraic Solutions and Hypotheses" is a valuable resource for mathematicians, researchers, and scholars interested in the qualitative theory of differential equations. It offers insightful solutions to an old problem and provides a comprehensive overview of the relevant theories and applications. The book's clear writing style, extensive examples, and comprehensive bibliography make it an essential tool for anyone seeking to advance their knowledge in this field.

Dimension: 234 x 156 (mm)
ISBN-13: 9781032017259