Skip to Main Content
 

Global Search Box

 
 
 

ETD Abstract Container

Abstract Header

Some Universality and Hypercyclicity Phenomena on Smooth Manifolds

Tuberson, Thomas Andrew
http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1657105322015704

Abstract Details

2022, Doctor of Philosophy (Ph.D.), Bowling Green State University, Mathematics/Mathematics (Pure).
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.
Kit Chan, Ph.D. (Committee Chair)
Julia Halo, Ph.D. (Other)
Juan Bes, Ph.D. (Committee Member)
Mihai Staic, Ph.D. (Committee Member)
82 p.
Mathematics
Functional Analysis; Operator Theory; Dynamics; Linear Dynamics; Universality; Hypercyclicity; Manifolds;

Recommended Citations

Citations

  • Tuberson, T. A. (2022). Some Universality and Hypercyclicity Phenomena on Smooth Manifolds [Doctoral dissertation, Bowling Green State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1657105322015704

    APA Style (7th edition)

  • Tuberson, Thomas. Some Universality and Hypercyclicity Phenomena on Smooth Manifolds. 2022. Bowling Green State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1657105322015704.

    MLA Style (8th edition)

  • Tuberson, Thomas. "Some Universality and Hypercyclicity Phenomena on Smooth Manifolds." Doctoral dissertation, Bowling Green State University, 2022. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1657105322015704

    Chicago Manual of Style (17th edition)

bgsu1657105322015704
65
© 2022, all rights reserved.
This open access ETD is published by Bowling Green State University and OhioLINK.