Advanced Search

The second order transverse bundle $T_{}^{2}M$ of a foliated manifold $M$ carries a natural structure of a smooth manifold over the algebra ${𝔻}^2$ of truncated polynomials of degree two in one variable. Prolongations of foliated mappings to second order transverse bundles are a partial case of more general ${𝔻}^2$-smooth foliated mappings between second order transverse bundles. We establish necessary and sufficient conditions under which a ${𝔻}^2$-smooth foliated diffeomorphism between two second order transverse bundles maps...