Almost Lie structures on an anchored Banach bundle

TL;DR

This paper generalizes the concept of almost Lie structures to Banach anchored bundles, establishing relations among them and applying the framework to mechanical systems like the Hilbert snake.

Contribution

It introduces a generalized formalism for almost Lie structures on Banach bundles and explores their applications in mechanical systems.

Findings

Established relations between almost Lie algebroids and almost differentials in Banach bundles.

Developed an adapted formalism for mechanical systems within this framework.

Illustrated the approach with the evolutionary problem of the Hilbert snake.

Abstract

Under appropriate assumptions, we generalize the concept of linear almost Poisson struc- tures, almost Lie algebroids, almost differentials in the framework of Banach anchored bundles and the relation between these objects. We then obtain an adapted formalism for mechanical systems which is illustrated by the evolutionary problem of the "Hilbert snake"