Stability Domain and Invariant Manifolds of 2d Area-Preserving Diffeomorphisms
Author: Giovannozzi, M.
Source: Celestial Mechanics and Dynamical Astronomy, Volume 68, Number 2, 1997 , pp. 177-192(16)
Abstract:We study the stability domain of generic 2D area-preserving polynomial diffeomorphisms. The starting point of our analysis is the study of the distribution of stable and unstable fixed points. We show that the location of fixed points and their stability type are linked to the degree of the polynomial map. These results are based on a classification Theorem for plane automorphisms by Friedland and Milnor. Then we discuss the problem of determining the domain in phase space where stable motion occurs. We show that the boundary of the stability domain is given by the invariant manifolds emanating from the outermost unstable fixed point of low period (one or two). This fact extends previous results obtained for reversible area-preserving polynomial maps of the plane. This analysis is based on analytical arguments and is supported by the results of numerical simulations.
Document Type: Regular Paper
Affiliations: INFN Sezione di Bologna, V. Irnerio 46, 40126 Bologna, Italy
Publication date: January 1, 1997