On some directions in the development of jet calculus

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.