Snakes and articulated arms in an Hilbert space

TL;DR

This paper illustrates advanced results on integrability and accessibility of vector field distributions in Banach and Hilbert spaces, generalizing finite-dimensional theorems to infinite-dimensional settings.

Contribution

It extends finite-dimensional accessibility theorems to separable Hilbert spaces using Banach manifold techniques and prior integrability results.

Findings

Generalization of a finite-dimensional accessibility theorem to Hilbert spaces

Illustration of integrability of distributions on Banach manifolds

Application of previous results to infinite-dimensional Hilbert space context

Abstract

The purpose of this paper is to give an illustration of results on integrability of distributions and orbits of vector fields on Banach manifolds obtained in [Pe] and [LaPe]. Using arguments and results of these papers, in the context of a separable Hilbert space, we give a generalization of a Theorem of accessibility contained in [Ha], [Ro] and proved for a finite dimensional Hilbert space