ウラジミール・アーノルド著／力学、統計学、ガロア体の射影幾何学 Dynamics, Statistics and Projective Geometry of Galois Fields

Arnold, V. I.

Cambridge University Press（2010/12発売）

• 製本 Hardcover:ハードカバー版／ページ数 90 p.／サイズ 10 b/w illus.
• 言語 ENG
• 商品コード 9780521872003
• DDC分類 512.32

基本説明

V. I. Arnold reveals some unexpected connections between such apparently unrelated theories as Galois fields, dynamical systems, ergodic theory, statistics, chaos and the geometry of projective structures on finite sets. The author blends experimental results with examples and geometrical explorations to make these findings accessible to a broad range of mathematicians, from undergraduate students to experienced researchers.

Full Description

V. I. Arnold reveals some unexpected connections between such apparently unrelated theories as Galois fields, dynamical systems, ergodic theory, statistics, chaos and the geometry of projective structures on finite sets. The author blends experimental results with examples and geometrical explorations to make these findings accessible to a broad range of mathematicians, from undergraduate students to experienced researchers.

Contents

Preface; 1. What is a Galois field?; 2. The organisation and tabulation of Galois fields; 3. Chaos and randomness in Galois field tables; 4. Equipartition of geometric progressions along a finite one-dimensional torus; 5. Adiabatic study of the distribution of geometric progressions of residues; 6. Projective structures generated by a Galois field; 7. Projective structures: example calculations; 8. Cubic field tables; Index.