On some directions in the development of jet calculus

TL;DR

This paper surveys key developments in jet calculus, introduces quasijets and jets of foliated manifolds, and presents new results on jets modulo multifoliations and their relation to $(R,S,Q)$-jets.

Contribution

It introduces quasijets, extends jets to foliated and multifoliate manifolds, and connects jets modulo multifoliations with $(R,S,Q)$-jets.

Findings

Jets are generalized to quasijets.

Jets of foliated and multifoliate manifolds are presented.

Jets modulo multifoliations are related to $(R,S,Q)$-jets.

Abstract

Two significant directions in the development of jet calculus are showed. First, jets are generalized to so-called quasijets. Second, jets of foliated and multifoliate manifold morphisms are presented. Although the paper has mainly a survey character, it also includes new results: jets modulo multifoliations are introduced and its relation to $(R,S,Q)$-jets is demonstrated.