Date on Master's Thesis/Doctoral Dissertation
Applied and Industrial Mathematics, PhD
Chaotic behavior in systems; Differentiable dynamical systems
All the common notions about dynamics in cascades - topological transitivity, periodic points, sensitive dependence, and so forth - can be formulated in the context of a general abelian semiflow. Many intricate results, such as the redundancy of Devaney chaos, remain true (with very minor qualifications) in this wider context. However, when we examine general monoid actions on a product space, it turns out that the topological and algebraic structure of N0 plays a large role in the preservation of chaotic properties. In order to obtain meaningful results in that arena, new ideas such as “directional” and “synnrec” are introduced, then applied.
Money, Chad, "Chaos in semiflows." (2015). Electronic Theses and Dissertations. Paper 2251.