Polynomial Automorphisms: and the Jacobian Conjecture: 190 (Progress in Mathematics, 190) - Hardcover

Van Den Essen, Arno

Hardcover

ISBN 10: 3764363509 ISBN 13: 9783764363505

Publisher: Birkhäuser, 2000

Synopsis

Motivated by some notorious open problems, such as the Jacobian conjecture and the tame generators problem, the subject of polynomial automorphisms has become a rapidly growing field of interest. This book, the first in the field, collects many of the results scattered throughout the literature. It introduces the reader to a fascinating subject and brings him to the forefront of research in this area. Some of the topics treated are invertibility criteria, face polynomials, the tame generators problem, the cancellation problem, exotic spaces, DNA for polynomial automorphisms, the Abhyankar-Moh theorem, stabilization methods, dynamical systems, the Markus-Yamabe conjecture, group actions, Hilbert's 14th problem, various linearization problems and the Jacobian conjecture. The work is essentially self-contained and aimed at the level of beginning graduate students. Exercises are included at the end of each section. At the end of the book there are appendices to cover used material from algebra, algebraic geometry, D-modules and Gröbner basis theory. A long list of ''strong'' examples and an extensive bibliography conclude the book.

About this title

Product Description:

Motivated by some notorious open problems, such as the Jacobian conjecture ansd the tame generators problem, the subject of polynomial automorphisms has become a rapidly growing field of interest. This text introduces the subject and collect many results together.Table of ContentsPart 1 Methods: preliminaries; derivations and polynomial automorphisms; invertibility criteria and inversion formulae; injective morphisms; the tame automorphism group of a polynomial ring; stabilisation methods; polynomial maps with nilpotent Jacobian. Part 2 Applications: applications of polynomial mappings to dynamical systems; group actions; the Jacobian conjecture. Appendices: some commutative algebra; some basic results from algebraic geometry; some results from Grobner basis theory; flatness; D-modules; special examples and counterexamples.

Review:

"...This book is a valuable reference for the study of polynomial automorphisms, due to its breadth of coverage and clarity of exposition."

--Mathematical Reviews

About this edition

• Publisher: Birkhäuser
• Publication date: 2000
• ISBN 10: 3764363509
• ISBN 13: 9783764363505
• Binding: Hardcover
• Number of pages: 347