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https://hdl.handle.net/2142/20479
Description
Title
Discrete multiple-valued dynamical systems
Author(s)
Lampe, Richard Elliot
Issue Date
1995
Doctoral Committee Chair(s)
Muncaster, Robert G.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
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.
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