UNITS - REMARKABLE POINTS IN DYNAMICAL-SYSTEMS

Authors
Citation
Jac. Gallas, UNITS - REMARKABLE POINTS IN DYNAMICAL-SYSTEMS, Physica. A, 222(1-4), 1995, pp. 125-151
Citations number
31
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physics
Journal title
ISSN journal
0378-4371
Volume
222
Issue
1-4
Year of publication
1995
Pages
125 - 151
Database
ISI
SICI code
0378-4371(1995)222:1-4<125:U-RPID>2.0.ZU;2-H
Abstract
In number theory, ''units'' are very special numbers characterized by having their norm equal to unity. So, in the real quadratic field Z(ro ot 3) the number -2 + root 3 similar or equal to -0.2679491924... is a unit because (-2 + root 3) (-2 - root 3) = 1. In this paper we determ ine precisely the numerical values of the coordinates of some points d efined by multiple intersections of domains of stability in the parame ter space of the Henon map and, in all cases considered for which anal ytical calculations were feasible, find that such intersection points are invariably defined by units and by simple functions of units. The very special points defined by units are analogous to the familiar mul ticritical points in phase diagrams. Some simple consequences of the p recise dynamics on the ground fields enforced by the equations of moti on are discussed.