Polynomial automorphisms : and the jacobian conjecture多项自守自同构
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作者： Arno van den Essen著
出 版 社：
出版时间： 2000-10-1字数：版次： 1页数： 329印刷时间： 2000/10/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9783764363505包装： 精装内容简介
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.
目录
Preface
Introduction
IMethods
1 Preliminaries
2 Derivations and polynomial automorphisms
3 Invertibility criteria and inversion formulae
4 Injective morphisms
5 The tame automorphism group of a polynomial ring
6 Stabilization Methods
7 Polynomial maps with nilpotent Jacobian
IIApplications
8 Applications of polynomial mappings to dynamical systems
9 Group actions
10 The Jacobian Conjecture
III Appendices
A Some commutative algebra
B Some basic results from algebraic geometry
C Some results from Grobner basis theory
D Flatness
E D-Modules
F Special examples and counterexamples
Bibliography
Authors Index
Index