Dynamics, Statistics and Projective Geometry of Galois Fields

V. I. Arnold reveals some unexpected connections between Galois fields and other apparently unrelated theories.

V. I. Arnold (Author)

9780521872003, Cambridge University Press

Hardback, published 2 December 2010

90 pages, 10 b/w illus.
23.5 x 15.5 x 1 cm, 0.27 kg

"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

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.

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.

Subject Areas: Nonlinear science [PBWR], Geometry [PBM], Number theory [PBH]