3:30 pm, Seminar hall
On the boundaries of the Arnold tongues
For a family of two-parameter analytic circle diffeomorphism, the space of the parameters can be partitioned according to the rotation number of the circle diffeomorphism corresponding to each parameter. An Arnold tongue of rotation number $\theta$ is defined as the collection of parameters for which each circle diffeomorphism with those parameters has rotation number $\theta$. Some results on the shapes and boundaries of these Arnold tongues will be discussed.