Discrete multiple-valued dynamical systems

In this paper we introduce the idea of multiple valued iteration theory. For a set X and family of functions ${\cal F} = \{ f\sb{i}\} \sb{i\in I}$ indexed by a countable set I, each $f\sb{i} : X \to X,$ we consider all possible ways of forming the $n\sp{th}$ iterate, for $n\in {\rm I\!N}.$ We study the dynamics of multiple valued maps which arise from functions of the form $B\sb{r}(x) = rx$ (mod 1) as maps of the interval. For these systems, we determine the structure of orbits and study their discrete time averages.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Lampe, Richard Elliot

Contributors dc:contributor

• Muncaster, Robert G.

• Mathematics

Statement dc:rights

• Copyright 1995 Lampe, Richard Elliot

Language dc:language

eng

Identifier

AAI9543639
(UMI)AAI9543639

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/20479