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Title:On *Categories of Cohesive, Active Sets and Other Dynamic Systems
Author(s):Wojtowicz, Ralph Leonard
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:It is shown that a category-theoretic definition of chaotic system applies not only to the Smale horseshoe, a standard chaotic system, but also to Conway's "Game of Life" automaton. Symbolic dynamics of the "Dining Philosophers" relational system is computed. A category composed of stochastic matrices is defined and some of its elementary properties are developed. A categorical variant of symbolic dynamics is applied to a finite stochastic process. Using point-wise Kan extension formulas, conditions ensuring existence of certain representations among categories of dynamic systems are proved.
Issue Date:2002
Type:Text
Language:English
Description:217 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2002.
URI:http://hdl.handle.net/2142/86808
Other Identifier(s):(MiAaPQ)AAI3070478
Date Available in IDEALS:2015-09-28
Date Deposited:2002


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