Spread polynomials, rotations and the butterfly effect

Details Spread polynomials, rotations and the butterfly effect Spread polynomials, rotations and the butterfly effect

2009-11-05

arxiv.org/abs/0911.1025v1

Mathematics

Classical Analysis and ODEs

14 pages, 3 figures

Scientific paper

The spread between two lines in rational trigonometry replaces the concept of angle, allowing the complete specification of many geometrical and dynamical situations which have traditionally been viewed approximately. This paper investigates the case of powers of a rational spread rotation, and in particular, a curious periodicity in the prime power decomposition of the associated values of the spread polynomials, which are the analogs in rational trigonometry of the Chebyshev polynomials of the first kind. Rational trigonometry over finite fields plays a role, together with non-Euclidean geometries.

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