SESIÓN DOBLE del seminario de sistemas dinámicos

Este viernes 23/10 tendremos una SESIÓN DOBLE del seminario de sistemas
dinámicos. Más abajo encontrarán título y resumen de cada charla.

13:00 - 14:00 Thusara Randula Ekanayake (USP). Salón 101.
14:00 - 14:30 Coffee break.
14:30 - 15:30 Barthélémy Doba (Sorbonne Université). Salón 101.


Thusara Randula Ekanayake (USP).

Título: Extensions of the Isometry Group of the Torus.

Resumen: Let $G$ be a subgroup of the group of diffeomorphisms of the
torus ${\mathbb{T}}^{2}={\mathbb{R}}^{2}/{\mathbb{Z}}^{2}$. Suppose that
the group of orientation preserving isometries of ${\mathbb{T}}^{2}$ is
a proper subgroup of $G$,  and that $G$ contains a $C^1$ diffeomorphism,
say $h$, isotopic to the identity and preserving the Lebesgue measure.
Assume also that $h$ is not an isometry. Then  there exists an element
$f\in G$ with positive topological entropy.


Barthélémy Doba (Sorbonne Université)

Titulo: Mumford compactness for PSL(3,R)-Hitchin representations.

Resumen: Given a closed, oriented and connected surface S of genus at
least two, the Hitchin component generalizes classical Teichmüller space
as a distinguished component of the PSL(3,R)-character variety. To any
such representation, one can define its systole and use Labourie's
boundary curve to define its Liouville volume.
In this talk, I will define the objects and explain (with some
consequences) an analog of the Mumford compactness theorem: the space of
Hitchin representations with Liouville volume bounded from above and
systole bounded from below is compact.