Relative periodic points of symplectic maps: persistence and bifurcations
نویسندگان
چکیده
منابع مشابه
Relative periodic points of symplectic maps: persistence and bifurcations
In this paper we study symplectic maps with a continuous symmetry group arising by periodic forcing of symmetric Hamiltonian systems. By Noether’s Theorem, for each continuous symmetry the symplectic map has a conserved momentum. We study the persistence of relative periodic points of the symplectic map when momentum is varied and also treat subharmonic persistence and relative subharmonic bifu...
متن کاملFixed points of symplectic periodic flows
The study of fixed points is a classical subject in geometry and dynamics. If the circle acts in a Hamiltonian fashion on a compact symplectic manifoldM , then it is classically known that there are at least dim M 2 +1 fixed points; this follows fromMorse theory for the momentum map of the action. In this paper we use Atiyah-Bott-Berline-Vergne (ABBV) localization in equivariant cohomology to p...
متن کاملInvariant curves near Hamiltonian Hopf bifurcations of D symplectic maps
In this paper we give a numerical description of the neighbourhood of a xed point of a symplectic map undergoing a transition from linear stability to complex instability i e the so called Hamiltonian Hopf bifurcation We have considered both the direct and inverse cases The study is based on the numerical computation of the Lyapunov families of invariant curves near the xed point We show how th...
متن کاملFixed Points and Periodic Points of Semiflows of Holomorphic Maps
Let φ be a semiflow of holomorphic maps of a bounded domain D in a complex Banach space. The general question arises under which conditions the existence of a periodic orbit of φ implies that φ itself is periodic. An answer is provided, in the first part of this paper, in the case in which D is the open unit ball of a J∗-algebra and φ acts isometrically. More precise results are provided when t...
متن کاملIsolated Fixed Points and Moment Maps of Symplectic Manifolds
Clearly every Hamiltonian circle action on a compact symplectic manifold must have fixed points, due to the existence of the maximum and minimum points of the moment map. The goal of this paper is, conversely, to investigate when a symplectic circle action on a compact symplectic manifold becomes Hamiltonian in terms of the fixed point data. As a consequence, we show that if the fixed point set...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Difference Equations and Applications
سال: 2006
ISSN: 1023-6198,1563-5120
DOI: 10.1080/10236190601045804