In this paper, by using of Frobenius theorem a relation between Lie subalgebras of the Lie algebra of a top space T and Lie subgroups of T(as a Lie group) is determined. As a result we can consider these spaces by their Lie algebras. We show that a top space with the finite number of identity elements is a C^{∞} principal fiber bundle, by this method we can characterize top spaces.

‎in this paper, we formulate the fourth order sturm-liouville problem (fslp) as a lie group matrix differential equation. by solving this ma- trix differential equation by lie group magnus expansion, we compute the eigenvalues of the fslp. the magnus expansion is an infinite series of multiple integrals of lie brackets. the approximation is, in fact, the truncation of magnus expansion and a gauss...

In this work we introduce a concept of expansiveness for actions connected Lie groups. We study some its properties and investigate implications expansiveness. the centralizer expansive CW-expansiveness pseudo-group actions. As an application, prove positiveness geometric entropy foliations group

Definition 1.1. [Ol] An m-dimensional manifold M is a topological space covered by a collection of open subsets Wα ⊂M (coordinate charts) and maps Xα : Wα → Vα ⊂ R one-to-one and onto, where Vα is an open, connected subset of R. (Wα,Xα) define coordinates on M. M is a smooth manifold if the maps Xαβ = Xβ ◦X−1 α , are smooth where they are defined, i.e. on Xα(Wα ∩Wβ) to Xβ(Wα ∩Wβ). Example 1.2. ...