University of Illinois at Urbana-Champaign
Global Analysis of Meromorphic Vector Fields in the Plane
Abstract
dc:descriptionThis work examines the behavior of meromorphic vector fields k(z) on the plane. The set of trajectories of k(z) whose maximal interval of definition is not all of R is called the incomplete set, and the analysis of k( z) then falls into two parts: the behavior of the incomplete set, and the behavior of the complement of the incomplete set. It is shown that zeros, poles and alpha and o limit points of k( z) all lie within the closure of the incomplete set. In a component of the complement of the closure of the incomplete set, all trajectories are either periodic with the same period (with the possible exception of one center lying within the component), or all trajectories are one to one trajectories.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2015
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Branson, William Balko
- Contributors dc:contributor
-
- Palmore, Julian
Subjects
dc:subject × 1Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- (MiAaPQ)AAI9971037
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/86993