V. I. Arnol'd, “Fermat Dynamics, Matrix Arithmetics, Finite Circles, and Finite Lobachevsky Planes”, Funktsional. Anal. i Prilozhen., 2004, Volume 38, Issue 1,Pages <nobr>1

This article is cited in 16 papers

Fermat Dynamics, Matrix Arithmetics, Finite Circles, and Finite Lobachevsky Planes

V. I. Arnol'd^ab

^a Steklov Mathematical Institute, Russian Academy of Sciences
^b Université Paris-Dauphine

Abstract: Congruences generalizing Fermat's little theorem are proved for the traces of powers of integer matrices. Their relations to Lobachevsky geometries over finite fields and combinatorics of the matrix squaring operation as well as to the corresponding Riemann surfaces with their Kepler cubes are discussed.

Keywords: arithmetics, symmetric function, de Sitter world, trace, Fermat's little theorem, Lobachevsky geometry, Kepler cube, Riemann surface.

UDC: 51

Received: 03.10.2003

DOI: 10.4213/faa92