Automorphisms of Affine Spaces

1. Front Matter

   Pages i-xix

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2. Polynomial Maps in Dimension n

   1. Front Matter

      Pages 1-1

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   2. Seven Lectures on Polynomial Automorphisms

      • Arno van den Essen

      Pages 3-39

   3. The Jacobian Conjecture: Some Steps towards Solution

      • Ludwik Drużkowski

      Pages 41-54

   4. Finite Automorphisms of Affine N-Space

      • Hanspeter Kraft, Gerald Schwarz

      Pages 55-66

   5. Polyomorphisms Conjugate to Dilations

      • Gary Meisters

      Pages 67-87

   6. On Separable Algebras over a U.F.D. and the Jacobian Conjecture in Any Characteristic

      • Kossivi Adjamagbo

      Pages 89-103

   7. Global Injectivity of Polynomial Maps Via Vector Fields

      • Anna Cima, Armengol Gasull, Jaume Llibre, Francesc Mañosas

      Pages 105-123

3. Two-dimensional Results

   1. Front Matter

      Pages 125-125

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   2. On the Markus-Yamabe Conjecture

      • Robert Feßler

      Pages 127-135

   3. Derivations Generated by Polynomials, Their Images and Complements of the Images

      • Yosef Stein

      Pages 137-144

   4. Normal Forms and the Jacobian Conjecture

      • David Wright

      Pages 145-156

   5. Radial Similarity of Newton Polygons

      • Charles Cheng, Stuart Wang

      Pages 157-167

   6. An Algorithm that Determines whether a Polynomial Map is Bijective

      • Charles Cheng, Stuart Wang

      Pages 169-176

4. Group Actions

   1. Front Matter

      Pages 177-177

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   2. Algebraic Aspects of Additive Group Actions on Complex Affine Space

      • James Deveney, David Finston

      Pages 179-190

   3. Quotients of Algebraic Group Actions

      • Harm Derksen

      Pages 191-200

   4. One-Parameter Subgroups and the Triangular Subgroup of the Affine Cremona Group

      • Gene Freudenburg

      Pages 201-213

   5. A Note on Nagata’s Automorphism

      • Jacques Alev

      Pages 215-221

5. Reactions on the conference

   1. Front Matter

      Pages 223-223

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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.

• Dimension
• Grad
• algebraic group
• algorithms
• dynamische Systeme
• ordinary differential equations
• partial differential equations

• Department of Mathematics, Catholic University of Nijmegen, Nijmegen, The Netherlands

  Arno Essen

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