Mathematics Ph.D. Dissertations
Some Universality and Hypercyclicity Phenomena on Smooth Manifolds
Date of Award
2022
Document Type
Dissertation
Degree Name
Doctor of Philosophy (Ph.D.)
Department
Mathematics/Mathematics (Pure)
First Advisor
Kit Chan (Committee Chair)
Second Advisor
Julia Halo (Other)
Third Advisor
Juan Bes (Committee Member)
Fourth Advisor
Mihai Staic (Committee Member)
Abstract
Hypercyclicity and universality have been extensively studied in the setting of Euclidean spaces. We show how to transfer such phenomena to the setting of smooth manifolds. We focus on operators on spaces of smooth functions defined on open subsets of smooth manifolds with an emphasis on partial differentiation operators. Furthermore, we provide a framework to extend the notions of universality and hypercyclicity to spaces of smooth functions defined on general smooth and complex manifolds. Motivated by our framework, we study the hypercyclicity phenomenon on differential forms on smooth manifolds. Finally, we construct a universal sequence of integral operators on spaces of differential forms defined on open subsets of smooth manifolds.
Recommended Citation
Tuberson, Thomas A., "Some Universality and Hypercyclicity Phenomena on Smooth Manifolds" (2022). Mathematics Ph.D. Dissertations. 86.
https://scholarworks.bgsu.edu/math_diss/86