منابع مشابه
Area-preserving Surface Diffeomorphisms
We prove some generic properties for Cr , r = 1, 2, . . . ,∞, areapreserving diffeomorphism on compact surfaces. The main result is that the union of the stable (or unstable) manifolds of hyperbolic periodic points are dense in the surface. This extends the result of Franks and Le Calvez [8] on S to general surfaces. The proof uses the theory of prime ends and Lefschetz fixed point theorem.
متن کاملHomoclinic Points for Area-preserving Surface Diffeomorphisms
We show a Cr connecting lemma for area-preserving surface diffeomorphisms and for periodic Hamiltonian on surfaces. We prove that for a generic Cr , r = 1, 2, . . ., ∞, area-preserving diffeomorphism on a compact orientable surface, homotopic to identity, every hyperbolic periodic point has a transversal homoclinic point. We also show that for a Cr, r = 1, 2, . . ., ∞ generic time periodic Hami...
متن کاملArea-preserving Diffeomorphisms and Nonlinear Integrable Systems
Present state of the study of nonlinear “integrable” systems related to the group of area-preserving diffeomorphisms on various surfaces is overviewed. Roles of area-preserving diffeomorphisms in 4-d self-dual gravity are reviewed. Recent progress in new members of this family, the SDiff(2) KP and Toda hierarchies, is reported. The group of area-preserving diffeomorphisms on a cylinder plays a ...
متن کاملHopf solitons and area preserving diffeomorphisms of the sphere
We consider a (3+1)-dimensional local field theory defined on the sphere S. The model possesses exact soliton solutions with non trivial Hopf topological charges, and infinite number of local conserved currents. We show that the Poisson bracket algebra of the corresponding charges is isomorphic to that of the area preserving diffeomorphisms of the sphere S. We also show that the conserved curre...
متن کاملSolvable Models for radiating Black Holes and Area - preserving Diffeomorphisms ∗
Solvable theories of 2D dilaton gravity can be obtained from a Liouville theory by suitable field redefinitions. In this paper we propose a new framework to generate 2D dilaton gravity models which can also be exactly solved in the semiclassical approximation. Our approach is based on the recently introduced scheme to quantize massless scalar fields coupled to 2D gravity maintaining invariance ...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2006
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-005-1514-3