WSU

Department of Mathematics
Topology Seminar 2006-2007

Wayne State University
College of Science


All talks are held Tuesdays at 2:00 PM in 1285 FAB, unless otherwise noted.
Contact Dan Isaksen (isaksen AT math.wayne.edu) for more information

All seminars
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Mathematics Department home page



Date: February 26, 2008

Speaker:  Ian Putnam, University of Victoria

Title: A homology theory for chaotic systems

Abstract: 

In the 1960's, Smale introduced the notion of an Axiom A system. These are diffeomorphisms of manifolds which display certain chaotic behaviour.  The chaotic part has a natural decomposition into irreducible parts called basic sets. One of Smale's great insights was that these sets usually failed to be submanifolds; they are now called fractals.  For zero-dimensional basic sets, Krieger introduced an invariant called the dimension group.  I will describe this and an extension of it to general basic sets using results of Bowen and some standard ideas from topology.