The investigators will continue their research involving measures of various kinds-Hausdorff, packing, Gibbs state, etc.; associated functions; and associated dimensions. These notions will be studied within the context of various dynamical systems as applied to Julia sets for example or to characterization of Jordan curves as repellers. They will use these techniques with regard to certain geometric objects and constructions, e.g. self-affine sets and self-- similar objects. This project involves research in ergodic theory. Ergodic theory in general concerns understanding the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. Under the heading "dynamics" can be placed the modern theory of how groups of abstract transformations act on smooth spaces. In this way, ergodic theory makes contact with geometry in its quest to classify flows on homogeneous spaces.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
9303888
Program Officer
Joe W. Jenkins
Project Start
Project End
Budget Start
1993-07-01
Budget End
1996-06-30
Support Year
Fiscal Year
1993
Total Cost
$80,000
Indirect Cost
Name
University of North Texas
Department
Type
DUNS #
City
Denton
State
TX
Country
United States
Zip Code
76203