Equivariant generating functions and periodic points (Q2741155)

Let an area-preserving map have a fixed point at the origin whose multipliers are \(n\)-th roots of unity, \(n\geq 2\). Then there is a function \(L\) whose critical points (excepting the origin) correspond to periodic points of the map of period \(n\). A maximum or minimum corresponds to an elliptic orbit and a saddle point correspond to a hyperbolic orbit. After a change of coordinates the function \(L\) is symmetric with respect to rotation by \(2\pi/n\).NEWLINENEWLINEFor the entire collection see [Zbl 0963.00030].