Geometric Configurations of Singularities of Planar Polynomial Differential Systems: A Global Classification in the Quadratic Case

This book provides a comprehensive study of finite and infinite singularities of planar polynomial differential systems, particularly focusing on quadratic systems. It includes the complete bifurcation diagram in the 12-parameter space of global geometrical configurations of singularities and their bifurcations, making it an essential resource for specialists, mathematicians, Ph.D. students, and postdoctoral fellows.

Format: Hardback
Length: 699 pages
Publication date: 18 June 2021
Publisher: Springer Nature Switzerland AG

This comprehensive book delves into the intricate study of finite and infinite singularities of planar polynomial differential systems, with a particular focus on quadratic systems. While results regarding the degenerate cases of singularities in quadratic systems have already been published elsewhere, the proofs for the more challenging remaining cases required considerable length. This book encompasses all cases, with half of its content dedicated to the last non-degenerate singularities.

The book features a comprehensive bifurcation diagram, spanning the 12-parameter space, that depicts global geometrical configurations of singularities in quadratic systems. The authors' groundbreaking findings offer a comprehensive global perspective on all singularities of quadratic systems, presenting them in invariant form and documenting their bifurcations. Moreover, a valuable software package is included, making the study of algebraic bifurcations significantly more efficient and time-saving.

Given its broad scope, this book will captivate specialists in polynomial differential systems, pure and applied mathematicians seeking to analyze bifurcation diagrams of families of such systems, Ph.D. students, and postdoctoral fellows.

Weight: 1226g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030505691
Edition number: 1st ed. 2021