منابع مشابه
Fixed 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 کاملFermat and the Number of Fixed Points of Periodic Flows
We obtain a general lower bound for the number of fixed points of a circle action on a compact almost complex manifold M of dimension 2n with nonempty fixed point set, provided the Chern number c1cn−1[M ] vanishes. The proof combines techniques originating in equivariant K-theory with celebrated number theory results on polygonal numbers, introduced by Pierre de Fermat. This lower bound confirm...
متن کاملFixed points of symplectic tranformations
Let (M,ω) be a closed symplectic manifold. Given a function H : M → R the Hamiltonian vector field XH determined by the Hamiltonian H is defined by the formula XH ω = −dH. Then LXHω = 0, and hence the flow generated by XH preserves the symplectic form ω. If one has a family of functions Ht : M → R, t ∈ [0, 1], one gets a family of Hamiltonian vector fields XHt which generate an isotopy ft : M →...
متن کاملThe Arnold Conjecture for Fixed Points of Symplectic Mappings and Periodic Solutions of Hamiltonian Systems
defines a family of diffeomorphisms on M which preserve the symplectic structure; i.e., for every t G R, (0*)*w = w, so that cj) is a symplectic diffeomorphism. DEFINITION. In the following we shall call a map on M Hamiltonian if it belongs to the flow 0* of any time-dependent exact Hamiltonian vector field on M. We remark that one can show that the set of Hamiltonian maps is the subgroup [...
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...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2010
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385710000295