Normal Forms for Three-parameter Families of Area-preserving Maps near an Elliptic Fixed Point

Abstract

We study dynamics of area-preserving maps in a neighborhood of an elliptic fixed point. We describe simplified normal forms for a fixed point of codimension 3. We also construct normal forms for a generic three-parameter family which contains such degeneracy and use normal form theory to describe generic bifurcations of periodic orbits in these families.