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

作者：Gelfreich Vassili^*; Gelfreikh Natalia

来源：Nonlinearity, 2014, 27(7): 1645-1667.

DOI：10.1088/0951-7715/27/7/1645

• area-preserving maps
• resonant fixed point
• normal forms
• bifurcation

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 families of area-preserving maps. We also derive a simplified normal form for a generic two-parametric family. The normal forms are used to analyse bifurcations of n-periodic orbits. In particular, for n %26gt;= 6 we find regions of parameters where the normal form has %26apos;meandering%26apos; invariant curves.

• 出版日期2014-7