Geometry, Topology and Dynamics Seminar
Konstantinos Efstathiou
University of Groningen
Hamiltonian monodromy: an overview and new perspectives
Abstract: Torus bundles are one of the most prominent features of integrable
Hamiltonian systems. The monodromy of such torus bundles over circles is
called Hamiltonian monodromy. In this talk I will give an overview of
Hamiltonian monodromy and discuss the development of the subject. I will
also present the ``geometric monodromy theorem'' which associates
monodromy to the focus-focus singular points of the Hamiltonian system.
Then I will consider the case of $n$-DOF (degree of freedom) integrable
Hamiltonian systems with global $\mathbb T^{n-1}$ actions and discuss
recent results obtained for such systems together with N. Martynchuk. In
particular, we have shown that monodromy in such systems is associated
to points where the isotropy is an $\mathbb S^1$ subgroup of the
$\mathbb T^{n-1}$ action. In the special case of $2$-DOF systems with an
$\mathbb S^1$ action this result implies that monodromy is associated to
the fixed points of the action. Finally we give a general and easy to
apply formula for computing monodromy in $n$-DOF systems.
Monday October 26, 2015 at 3:00 PM in SEO 636