Automorphisms of Affine Spaces: Proceedings of a Conference held in Curaçao (Netherlands Antilles), July 4–8, 1994, under auspices of the Caribbean Mathematical Foundation (CMF)

__Automorphisms of Affine Spaces__ describes the latest results concerning several conjectures related to polynomial automorphisms: the Jacobian, real Jacobian, Markus-Yamabe, Linearization and tame generators conjectures. Group actions and dynamical systems play a dominant role. Several contributions are of an expository nature, containing the latest results obtained by the leaders in the field. The book also contains a concise introduction to the subject of invertible polynomial maps which formed the basis of seven lectures given by the editor prior to the main conference. __Audience__: A good introduction for graduate students and research mathematicians interested in invertible polynomial maps. Front Matter....Pages i-xix Front Matter....Pages 1-1 Seven Lectures on Polynomial Automorphisms....Pages 3-39 The Jacobian Conjecture: Some Steps towards Solution....Pages 41-54 Finite Automorphisms of Affine N -Space....Pages 55-66 Polyomorphisms Conjugate to Dilations....Pages 67-87 On Separable Algebras over a U.F.D. and the Jacobian Conjecture in Any Characteristic....Pages 89-103 Global Injectivity of Polynomial Maps Via Vector Fields....Pages 105-123 Front Matter....Pages 125-125 On the Markus-Yamabe Conjecture....Pages 127-135 Derivations Generated by Polynomials, Their Images and Complements of the Images....Pages 137-144 Normal Forms and the Jacobian Conjecture....Pages 145-156 Radial Similarity of Newton Polygons....Pages 157-167 An Algorithm that Determines whether a Polynomial Map is Bijective....Pages 169-176 Front Matter....Pages 177-177 Algebraic Aspects of Additive Group Actions on Complex Affine Space....Pages 179-190 Quotients of Algebraic Group Actions....Pages 191-200 One-Parameter Subgroups and the Triangular Subgroup of the Affine Cremona Group....Pages 201-213 A Note on Nagata’s Automorphism....Pages 215-221 Front Matter....Pages 223-223 On a Question of Yosef Stein....Pages 225-229 A Counterexample to a Conjecture of Meisters....Pages 231-233 Back Matter....Pages 235-243