[Todos CMAT] Seminario de Sistemas Dinámicos

[seminarios en cmat.edu.uy]

Seminario de Sistemas Dinámicos
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Título: "CONSERVATIVE SURFACE HOMEOMORPHISMS WITH FINITELY MANY PERIODIC POINTS"

Expositor: Patrice Le Calvez (CNRS-IMJ)

Resumen:
 
We give a characterization of homeomorphisms $f$ of a closed surface of genus
$\geq 2$ with no wandering point that have finitely many periodic points. The
main result is the fact that there exists an integer $q$ such that the periodic
points of $f^q$ are fixed and $f^q$ is isotopic to the identity relative to its
fixed point set. The emblematic way to construct such an example is to start
with the time one map of a flow of minimal direction for a translation surface,
to add finitely many stopping points and to lift this map to a finite covering.
The main result in the proof is that every homeomorphism with no wandering
point, isotopic to a Dehn twist map, has infinitely many periodic points. Such a
result was known for a generic area preserving diffeomorphism in the isotopy
class. To extend this result, obtained with Martin Sambarino, to the general
case, one needs to introduce a ``forcing lemma'' , very similar to a forcing
result obtained with Fabio Tal in the case of maps isotopic to the identity.
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Viernes 20/5 a las 14:30, Salón de seminarios del IMERL

Contacto: León Carvajales - lcarvajales en cmat.edu.uy
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Link para seguir por zoom:
https://us06web.zoom.us/j/89701329574?pwd=K2JrNUNxTHZSVzN2cWVZWTRVdGc1QT09
Meeting ID: 897 0132 9574   Passcode: 984818   -------------   Próxima semana:
Sergio Fenley (FSU)
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