Sven Sandfeldt: On local Rigidity of Some Lie Group Actions
Time: Thu 2020-05-14 10.30
In the theory of smooth dynamical systems an important problem is the classification of smooth dynamical systems up to smooth conjugacy. A particular type of classification is the local classification about some given dynamical system. One way to give a local classification about some system is to show that that system is locally rigid, that is: That every system close to the given system is conjugated to a coordinate change of the given system. In this presentation we discuss applications of the Nash-Moser inverse function theorem when proving that a dynamical system is locally rigid. Using the Nash-Moser inverse function theorem we give a sufficient condition for local rigidity, and in extension we give a sufficient condition for a local classification. We also discuss the special case when the action is homogeneous in which case we obtain a stronger result.