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Lectures
Seminar information archive ～04/24｜Next seminar｜Future seminars 04/25～
2013/03/06
16:00-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)
Frederic Le Roux (Institut de Mathematiques de Jussieu, Universite Pierre et Marie Curie)
The rotation set around a fixed point for surface homeomorphisms. (ENGLISH)
Frederic Le Roux (Institut de Mathematiques de Jussieu, Universite Pierre et Marie Curie)
The rotation set around a fixed point for surface homeomorphisms. (ENGLISH)
[ Abstract ]
We propose two definitions of a local rotation set. As applications, one
gets some criteria for the existence of periodic orbits, and a clear
explanation of Gambaudo-Le Calvez-Pecou's version of the Naishul theorem:
for surface diffeomorphisms, the rotation number of the derivative at a
fixed point which is not a sink nor a source is a topological invariant.
Tha local rotation set also provide an unexpected topological
characterization for the parabolic fixed points of holomorphic maps.
We propose two definitions of a local rotation set. As applications, one
gets some criteria for the existence of periodic orbits, and a clear
explanation of Gambaudo-Le Calvez-Pecou's version of the Naishul theorem:
for surface diffeomorphisms, the rotation number of the derivative at a
fixed point which is not a sink nor a source is a topological invariant.
Tha local rotation set also provide an unexpected topological
characterization for the parabolic fixed points of holomorphic maps.
