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Title:Discrete multiple-valued dynamical systems
Author(s):Lampe, Richard Elliot
Doctoral Committee Chair(s):Muncaster, Robert G.
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract: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.
Issue Date:1995
Type:Text
Language:English
URI:http://hdl.handle.net/2142/20479
Rights Information:Copyright 1995 Lampe, Richard Elliot
Date Available in IDEALS:2011-05-07
Identifier in Online Catalog:AAI9543639
OCLC Identifier:(UMI)AAI9543639


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