Admissible vector fields and related diffusions on infinite-dimensional manifolds

Vector Fields on Manifolds

where n = dim M and 6» = ith Betti number of M ( = dim of Hi(M; Q)). Thus the geometric property of M having a nonzero vector field is expressed in terms of the algebraic invariant xM. We will discuss extensions of this idea to vector ^-fields, fields of ^-planes, and foliations of manifolds. All manifolds considered will be connected, smooth and without boundary; all maps will be continuous. F...

Two-dimensional global manifolds of vector fields.

We describe an efficient algorithm for computing two-dimensional stable and unstable manifolds of three-dimensional vector fields. Larger and larger pieces of a manifold are grown until a sufficiently long piece is obtained. This allows one to study manifolds geometrically and obtain important features of dynamical behavior. For illustration, we compute the stable manifold of the origin spirall...

Admissible vector fields and quasi-invariant measures∗

Triangulated Infinite-dimensional Manifolds

In this paper we extend almost all the results on infinite-dimensional Fréchet manifolds to apply to manifolds modeled on some 2̂ ( = {#£^1 at most finitely many of the coordinates of x are nonzero } ) and we show (Theorem 14) that each /^-manifold has a unique completion to an /2-manifold. (We use h to stand for the Hubert space of all square-summable sequences of some infinite cardinality 31. ...

Infinite–dimensional Diffusions as Limits of Random Walks on Partitions

The present paper originated from our previous study of the problem of harmonic analysis on the infinite symmetric group S∞. This problem leads to a family {Pz} of probability measures, the z–measures, which depend on the complex parameter z ∈ C. The z–measures live on the Thoma simplex, an infinite–dimensional compact space Ω which is a kind of dual object to the group S∞. The aim of the paper...