Actions with globally hypoelliptic leafwise Laplacian
September 18, 2013
3:00pm PGH 646
Abstract
One question frequently asked in dynamics is: what can be said about
perturbations of a given dynamical system? Is any classification of
perturbations possible? For \(\bf R\)-actions, i.e. flows, a reasonable
classification exists only for flows tangent to Diophantine vector fields
on tori. This is part of the classical Kolmogorov-Arnold-Moser (KAM) result
from 1960's. These flows have a very strong property of global
hypoellipticity. In this talk I will discuss this property for general
differential operators and the consequences of having a higher rank abelian
action whose leafwise Laplacian is globally hypoelliptic. Conjecturally for
such actions one should be able to classify perturbations. This has been
confirmed for a class of actions on 2-step nilmanifolds.
Webmaster University of Houston
---
Last modified: April 11 2016 - 18:14:43