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Relative Nielsen Theory and Surface Tangles
by
Pieter Collins
University of California, Berkeley
We give a Nielsen theory for self-maps of topological pairs (X, Y) where X is a compact absolute neighbourhood retract and Y is a closed subset of X. This theory is particularly useful for finding periodic orbits, and gives symbolic dynamics in terms of a partition into components of X-Y. We apply this theory to obtain interesting results for surface maps with homoclinic/heteroclinic tangles, including symbolic dynamics and lower bounds on topological entropy.
Date received: June 9, 1999
Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacl-69.