9500803 Feldman This project involves many facets of work on probability theory and ergodic theory. The research includes work on the following projects: A classification of filtrations of stochastic processes; Zero-one asymptotic properties of averages of functions transformed under ergodic measure preserving transformations; Cofiltrations and ergodic group actions; Reparametrization for Euclidean group actions and for foliations; Ergodic properties of multiplication on the circle. Collectively, these projects cover a broad portion of the current ergodic theory research landscape. Ergodic theory in general concerns understanding the average long-term behavior of systems that are too complicated or chaotic to be followed in real time. Under the heading of "dynamics" can be placed the modern theory of how repeated applications of transformations effect measurable quantities. In this way, groups of transformations and abstract measure theory form the mathematical cornerstones of ergodic theory. This proposal involves the leading edge of the mathematics of ergodic theory. ***

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
9500803
Program Officer
Bruce P. Palka
Project Start
Project End
Budget Start
1995-07-01
Budget End
2000-06-30
Support Year
Fiscal Year
1995
Total Cost
$24,047
Indirect Cost
Name
University of California Berkeley
Department
Type
DUNS #
City
Berkeley
State
CA
Country
United States
Zip Code
94704