An Integrable Flow on a Family of HilbertGrassmanniansRodrigo
نویسنده
چکیده
Various researchers have studied examples of innnite-dimensional dynamical systems. In most of the cases, the phase space consisted of a Hilbert or Banach space or a Frechet space of functions. In this article we propose to study a dynamical system, namely the geodesic ow, over more structurally complex manifolds, the tangent bundles of a family of Hilbert Grassmannians. Using the high degree of symmetry of the spaces and the methods of Thimm 9] and Ii and Watanabe 3] we prove that the geodesic ow is integrable. In the process we determine a spectral invariant a la Moser 5] which completely describes the behavior of the geodesics of the Hilbert Grassmannians. As a result we demonstrate the diierence in complexity between the various ranked Hilbert Grassmannians.
منابع مشابه
Two-wavelet constants for square integrable representations of G/H
In this paper we introduce two-wavelet constants for square integrable representations of homogeneous spaces. We establish the orthogonality relations fo...
متن کاملHierarchy of Integrable Geodesic Flows
A family of integrable geodesic flows is obtained. Any such a family corresponds to a pair of geodesically equivalent metrics.
متن کاملON CONVERGENCE THEOREMS FOR FUZZY HENSTOCK INTEGRALS
The main purpose of this paper is to establish different types of convergence theorems for fuzzy Henstock integrable functions, introduced by Wu and Gong cite{wu:hiff}. In fact, we have proved fuzzy uniform convergence theorem, convergence theorem for fuzzy uniform Henstock integrable functions and fuzzy monotone convergence theorem. Finally, a necessary and sufficient condition under which th...
متن کاملOn a class of integrable systems with a cubic first integral
A few years ago Selivanova gave an existence proof for some integrable models, in fact geodesic flows on two dimensional manifolds, with a cubic first integral. However the explicit form of these models hinged on the solution of a nonlinear third order ordinary differential equation which could not be obtained. We show that an appropriate choice of coordinates allows for integration and gives t...
متن کاملIntegrable geodesic flows and Multi-Centre versus Bianchi A metrics
It is shown that most, but not all, of the four dimensional metrics in the MultiCentre family with integrable geodesic flow may be recognized as belonging to spatially homogeneous Bianchi type A metrics. We show that any diagonal bi-axial Bianchi II metric has an integrable geodesic flow, and that the simplest hyperkähler metric in this family displays a finite dimensional W-algebra for its obs...
متن کامل