On *Categories of Cohesive, Active Sets and Other Dynamic Systems
Wojtowicz, Ralph Leonard
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https://hdl.handle.net/2142/86808
Description
Title
On *Categories of Cohesive, Active Sets and Other Dynamic Systems
Author(s)
Wojtowicz, Ralph Leonard
Issue Date
2002
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
"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."
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