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Kyoto Dynamics Days 5 Trellis and related topics

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.
January 26
2:00-3:30 Pieter Collins (CWI & Kyoto Univ.)
Lectures on Homoclinic Dynamics and Trellises (1)
Introduction to Nielsen-Thurston 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 fixed-point
index and the Nielsen fixed-point theory. I will then give Thurston's classification of isotopy classes
of surface homeomorphisms. I will next discuss the dynamical properties of pseudo-Anosov
diffeomorphisms and the Thurston minimal representative. Finally, I will outline Bestivaand Handel's
algorithm for the computing train-tracks for pseudo-Anosov 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 fixed-point
theory are directly useful, and most of the others can be adapted from the periodic case to the


Source: Arai, Zin - Department of Mathematics, Kyoto University


Collections: Mathematics