Dynamics, Statistics and Projective Geometry of Galois Fields

V. I. Arnold

doi:10.1017/CBO9780511975783

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.

"Throughout, Arnold's characteristic style of writing and thinking are evident. Ideas, intuitions, and well-presented examples abound, joined in only a few places by formal proofs... students and working mathematicians will find it accessible, provoctive, and maybe even inspiring."
Rafe Jones, Mathematical Reviews

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Dynamics, Statistics and Projective Geometry of Galois Fields

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

Preface
pp ix-x

1 - What is a Galois field?
pp 1-8

2 - The organisation and tabulation of Galois fields
pp 9-16

3 - Chaos and randomness in Galois field tables
pp 17-23

4 - Equipartition of geometric progressions along a finite one-dimensional torus
pp 24-36

5 - Adiabatic study of the distribution of geometric progressions of residues
pp 37-43

6 - Projective structures generated by a Galois field
pp 44-53

7 - Projective structures: example calculations
pp 54-69

8 - Cubic field tables
pp 70-79

Index
pp 80-80

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Dynamics, Statistics and Projective Geometry of Galois Fields

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