コロキウム

We discuss non-existence of invariant curves of area-preserving maps. In the case that the parameter of the standard map is close to zero, KAM theorem shows the existence of a number of invariant closed curves. Aubry, Mather, MacKay, and Jungreis showed the non-existence of invariant closed curves in the case that the parameter is large. In this talk, we extend Mather’s result and show non-existence of invariant curves for the standard map by using a rigorous numerical scheme.