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.
Keywords:
area-preserving maps, resonant fixed point, normal form, bifurcation
Citation:
Gelfreikh N. G., Normal Forms for Three-parameter Families of Area-preserving Maps near an Elliptic Fixed Point, Regular and Chaotic Dynamics,
2018, Volume 23, Number 3,
pp. 273-290