Date on Master's Thesis/Doctoral Dissertation


Document Type

Doctoral Dissertation

Degree Name

Ph. D.



Degree Program

Applied and Industrial Mathematics, PhD

Committee Chair

Miller, Alica

Committee Co-Chair (if applicable)

Kantardzic, Mehmed

Committee Member

Kantardzic, Mehmed

Committee Member

Riedel, Thomas

Committee Member

Sahoo, Prasanna

Committee Member

Tone, Cristina


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.