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 gives 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: Paperback / softback
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 overview of the topic. Chapter 1 introduces the problem and highlights its historical significance. Chapter 2 explores the mathematical background necessary for understanding the concepts presented later. Chapters 3 and 4 present the main results and theoretical developments, respectively. Chapter 5 concludes the book by discussing potential future research directions and offering insights into the broader implications of the findings.

With its clear and concise writing style, this book is accessible to a wide range of readers, including those with a basic understanding of differential equations and mathematics. It serves as a valuable resource for both academicians and practitioners seeking to deepen their knowledge in this field. The Center and Focus Problem: Algebraic Solutions and Hypotheses is a testament to the enduring contributions of M. N. Popa and V.V. Pricop to the study of differential equations and their applications.

Weight: 348g
Dimension: 215 x 252 x 20 (mm)
ISBN-13: 9781032044101