 
Summary: Kyoto Dynamics Days 5
Trellis and related topics
January 26  27, 2005
Department of Mathematics, Kyoto University
Large Meeting Room in Math. Department Bldg.
Program
January 26
2:003:30 Pieter Collins (CWI & Kyoto Univ.)
Lectures on Homoclinic Dynamics and Trellises (1)
Introduction to NielsenThurston Theory
Abstract: In the first talk, I will review the theory of surface homeomorphisms developed
primary by J. Nielsen and W. Thurston. I will first give an overview of the Lefschetz fixedpoint
index and the Nielsen fixedpoint theory. I will then give Thurston's classification of isotopy classes
of surface homeomorphisms. I will next discuss the dynamical properties of pseudoAnosov
diffeomorphisms and the Thurston minimal representative. Finally, I will outline Bestivaand Handel's
algorithm for the computing traintracks for pseudoAnosov isotopy classes.
The results reviewed here is important for the development of a theory for homoclinic
dynamics of surface diffeomorphisms. The theory for periodic dynamics gives a scheme to follow in
developing a theory for homoclinic dynamics. Some of the results, especially those on fixedpoint
theory are directly useful, and most of the others can be adapted from the periodic case to the
