5 papers
Approximating continuous function on orbit spaces
Qianqian Xia
In this paper we study a subclass of subcartesian space-the orbit space of a proper action of Lie group on smooth manifold. We show that continuous functions on orbit space can be…
On controlled invariance for regular distributions
Qianqian Xia
This paper considers the problem of controlled invariance of involutive regular distribution, both for smooth and real analytic cases. After a review of some existing work, a preci…
Smooth distributions on subcartesian spaces are globally finitely generated
Qianqian Xia
We prove that a connected subcartesian space admits embedding in a Euclidean space. The Whitney Embedding Theorem is then stated as a corollary of our result. Based on the above re…
Morphisms of tautological control systems
Qianqian Xia
In this paper, we investigate morphisms of tautological control systems. Given a tautological control system on the manifold N and a mapping , we study e…
Quotients of affine connection control systems
Qianqian Xia, Zhiyong Geng
In this paper, we investigate the existence of a subclass of quotients of affine connection control systems, which preserve the mechanical structures. Both local and global suffici…