Geometric Configurations of Singularities of Planar Polynomial Differential Systems : A Global Classification in the Quadratic Case / by Joan C. Artés, Jaume Llibre, Dana Schlomiuk, Nicolae Vulpe.

Format:

Book

Author/Creator:

Artés, Joan C., 1961- author.

Language:

English

Subjects (All):

Global analysis (Mathematics).

Manifolds (Mathematics).

Differential equations.

Global Analysis and Analysis on Manifolds.

Differential Equations.

Local Subjects:

Global Analysis and Analysis on Manifolds.

Differential Equations.

Physical Description:

1 online resource (xii, 699 pages)

Edition:

1st ed. 2021.

Place of Publication:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2021.

Summary:

This book addresses the global study of finite and infinite singularities of planar polynomial differential systems, with special emphasis on quadratic systems. While results covering the degenerate cases of singularities of quadratic systems have been published elsewhere, the proofs for the remaining harder cases were lengthier. This book covers all cases, with half of the content focusing on the last non-degenerate ones. The book contains the complete bifurcation diagram, in the 12-parameter space, of global geometrical configurations of singularities of quadratic systems. The authors’ results provide - for the first time - global information on all singularities of quadratic systems in invariant form and their bifurcations. In addition, a link to a very helpful software package is included. With the help of this software, the study of the algebraic bifurcations becomes much more efficient and less time-consuming. Given its scope, the book will appeal tospecialists on polynomial differential systems, pure and applied mathematicians who need to study bifurcation diagrams of families of such systems, Ph.D. students, and postdoctoral fellows.

Contents:

Part I

Polynomial differential systems with emphasis on the quadratic ones

1 Introduction

2 Survey of results on quadratic differential systems

3 Singularities of polynomial differential systems

4 Invariants in mathematical classification problems

5 Invariant theory of planar polynomial vector fields

6 Main results on classifications of singularities in QS

7 Classifications of quadratic systems with special singularities

Part II

8 QS with finite singularities of total multiplicity at most one

9 QS with finite singularities of total multiplicity two

10 QS with finite singularities of total multiplicity three

11 QS with finite singularities of total multiplicity four

12 Degenerate quadratic systems

13 Conclusions.

Notes:

Includes bibliographical references and index.

ISBN:

3-030-50570-7