Conjugation of linear vector fields on Lie groups
نویسندگان
چکیده
In this paper we study a classification of linear systems on Lie groups with respect the conjugacy of the corresponding flows. We also describe stability according to Lyapunov exponents.
منابع مشابه
Harmonicity and Minimality of Vector Fields on Lorentzian Lie Groups
We consider four-dimensional lie groups equipped with left-invariant Lorentzian Einstein metrics, and determine the harmonicity properties of vector fields on these spaces. In some cases, all these vector fields are critical points for the energy functional restricted to vector fields. We also classify vector fields defining harmonic maps, and calculate explicitly the energy of t...
متن کاملThe Lie Algebra of Smooth Sections of a T-bundle
In this article, we generalize the concept of the Lie algebra of vector fields to the set of smooth sections of a T-bundle which is by definition a canonical generalization of the concept of a tangent bundle. We define a Lie bracket multiplication on this set so that it becomes a Lie algebra. In the particular case of tangent bundles this Lie algebra coincides with the Lie algebra of vector fie...
متن کاملGROUPOID ASSOCIATED TO A SMOOTH MANIFOLD
In this paper, we introduce the structure of a groupoid associated to a vector field on a smooth manifold. We show that in the case of the $1$-dimensional manifolds, our groupoid has a smooth structure such that makes it into a Lie groupoid. Using this approach, we associated to every vector field an equivalence relation on the Lie algebra of all vector fields on the smooth...
متن کاملEquivalence of Control Systems with Linear Systems on Lie Groups and Homogeneous Spaces
The aim of this paper is to prove that a control affine system on a manifold is equivalent by diffeomorphism to a linear system on a Lie group or a homogeneous space if and only the vector fields of the system are complete and generate a finite dimensional Lie algebra. A vector field on a connected Lie group is linear if its flow is a one parameter group of automorphisms. An affine vector field...
متن کاملClassification of Lie Subalgebras up to an Inner Automorphism
In this paper, a useful classification of all Lie subalgebras of a given Lie algebraup to an inner automorphism is presented. This method can be regarded as animportant connection between differential geometry and algebra and has many applications in different fields of mathematics. After main results, we have applied this procedure for classifying the Lie subalgebras of some examples of Lie al...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016