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Discrete multiple-valued dynamical systems

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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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