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Minimal sets of periods for Morse--Smale diffeomorphisms on connected compact surfaces without boundary
Jaume Llibre 教授,Universitat Autonoma de Barcelona,西班牙科学院院士
2018-01-01 12:13  华东师范大学

报告人:Jaume Llibre 教授
题目:Minimal sets of periods for Morse--Smale diffeomorphisms on connected compact surfaces without boundary
时间:2010年11月4日,10:30-11:30
地点:闵行数学楼102报告厅

ABSTRACT:
We study the minimal set of (Lefschetz) periods of the C^1 Morse-Smale diffeomorphisms on a (orientable or not) compact surface without boundary inside its class of homology. In fact our study extends to the C^1 diffeomorphisms on these surfaces having finitely many periodic orbits all of them hyperbolic and with the same action on the homology as the Morse-Smale diffeomorphisms.
We mainly have two kind of results. First we completely characterize the minimal sets of periods for the C^1 Morse-Smale diffeomorphisms on a compact surface without boundary of genus g=0,1,...,3 for orientable surfaces and genus g=1,2,...,9 for non-orientable ones. But the proof of these results provides an algorithm for characterizing these minimal sets of periods for the C^1 Morse-Smale diffeomorphisms on compact surfaces without boundary of arbitrary genus.
Second we study what kind of subsets of positive integers can be minimal sets of periods of the C^1 Morse-Smale diffeomorphisms on a compact surface without boundary.

Llibre教授简介:
Jaume Llibre is a professor of Universitat Autonoma de Barcelona
He is the member of Academy of Science of Spain(西班牙科学院院士)
In 2009 he obtained the highest lever prize of spain awarded to top
10 professors of spain in each year