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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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