The Gauss Map and Resistive Networks
by
Hei-Chi Chan
University of Illinois at Springfield

In the early 1800s, Gauss, in his letters to Laplace, mentioned a certain interval map that he was studying. Gauss obtained some partial results but he was not too satisfied with the outcome, as some crucial questions were still unanswered at that time. This map, which is now known as the Gauss map, is related to the metrical theory of continued fraction. In the early part of the 20^th century, Kusmin, Lévy and others took on the same problem and broke new ground in this area. To this day the Gauss map has fascinated researchers from various branches of mathematics and science: it is ergodic with respect to a known invariant measure and it has applications in computer science, in cosmology and in chaos theory. In this talk, I will talk about its application in resistive networks and survey some of its recent generalizations.

Date received: February 21, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cakr-42.