Simplified normal forms near a degenerate elliptic fixed point in two-parametric families of area-preserving maps

Abstract

We derive simplified normal forms for an area-preserving map in a neighbourhood of a degenerate resonant elliptic fixed point. Such fixed points appear in generic two-parameter families of area-preserving maps. We also derive a simplified normal form for a generic two-parametric unfolding. The normal forms are used to analyse bifurcations of $n$-periodic orbits. In particular, for $n\ge 6$ we find regions of parameters where the normal form has "meandering'' invariant curves.

References in corpus (1)

• Unique resonant normal forms for area preserving maps at an elliptic fixed point

Cited by in corpus (3)

• Parametric normal form classification for Eulerian and rotational non-resonant double Hopf singularities
• On local and global aspects of the 1:4 resonance in the conservative cubic Hénon maps
• Normal forms for three-parametric families of area-preserving maps near an elliptic fixed point