Géométrie et Systèmes Dynamiques

Groups of homeomorphisms of the line with a finite number of fixed points


Salle B318 (IMB)

Salle B318


The goal of my talk will be to address the question: "which groups of increasing homeomorphisms of the line have at most N fixed points?". This question already has a partial answer given by the Hölder's Theorem (for the case N=0) and the Solodov's Theorem (for the case N=1) which classifies, unless than a semi-conjugation, all the groups that satisfy this statement. However, this question was still completely open for cases N>1.
In this talk I will present a new result that classifies all the groups that satisfy the statement for the case N=2, and some new examples of groups with N>2. For that, it will be necessary to introduce the concept of Orbit Opening as a semi-conjugation of groups of homeomorphisms, and the complete statements of Hölder's and Solodov's Theorems.
Your browser is out of date!

Update your browser to view this website correctly. Update my browser now