Experimental Mathematics

Informal remarks on the orbit structure of discrete approximations to chaotic maps

Oscar E. Lanford III

Full-text: Open access

Abstract

We report the results of some computer experiments on the orbit structure of the discrete maps on a finite set which arise when an expanding map of the circle is iterated "naively" on the computer. We also comment on what mathematical questions ought to be answered in order to account for the reliability in practice of orbit following on the computer as an indicator of the ergodic properties of the underlying map.

Article information

Source
Experiment. Math., Volume 7, Issue 4 (1998), 317-324.

Dates
First available in Project Euclid: 14 March 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1047674149

Mathematical Reviews number (MathSciNet)
MR1678095

Zentralblatt MATH identifier
0922.58042

Subjects
Primary: 37E05: Maps of the interval (piecewise continuous, continuous, smooth)
Secondary: 34D45: Attractors [See also 37C70, 37D45] 37E15: Combinatorial dynamics (types of periodic orbits)

Citation

Lanford III, Oscar E. Informal remarks on the orbit structure of discrete approximations to chaotic maps. Experiment. Math. 7 (1998), no. 4, 317--324. https://projecteuclid.org/euclid.em/1047674149


Export citation