Abstract: We justify the averaging principle for slow fast systems in the case where the frozen motion is ergodic on almost every level set. We then discuss the rate of convergence in the important case where the fast motion is quasiperiodic
Abstract: Motivated by the question of M. Kac: Can you hear the shape of a drum? We introduce the Laplace spectrum and the length spectrum for convex planar domains. After showing a connection between the two spectra we shall discuss problems of spectral rigidity, namely, if it is possible to smoothly deform a domain without changing its spectra.