ترغب بنشر مسار تعليمي؟ اضغط هنا

On geodesic flows with symmetries and closed magnetic geodesics on orbifolds

115   0   0.0 ( 0 )
 نشر من قبل Luca Asselle
 تاريخ النشر 2017
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

Let $Q$ be a closed manifold admitting a locally-free action of a compact Lie group $G$. In this paper we study the properties of geodesic flows on $Q$ given by Riemannian metrics which are invariant by such an action. In particular, we will be interested in the existence of geodesics which are closed up to the action of some element in the group $G$, since they project to closed magnetic geodesics on the quotient orbifold $Q/G$.



قيم البحث

اقرأ أيضاً

145 - I.A. Taimanov 2016
The problem of the existence of an additional (independent on the energy) first integral, of a geodesic (or magnetic geodesic) flow, which is polynomial in momenta is studied. The relation of this problem to the existence of nontrivial solutions of s tationary dispersionless limits of two-dimensional soliton equations is demonstrated. The nonexistence of an additional quadratic first integral is established for certain classes of magnetic geodesic flows.
163 - Weisheng Wu 2021
In this article, we consider a closed rank one Riemannian manifold $M$ without focal points. Let $P(t)$ be the set of free-homotopy classes containing a closed geodesic on $M$ with length at most $t$, and $# P(t)$ its cardinality. We obtain the follo wing Margulis-type asymptotic estimates: [lim_{tto infty}#P(t)/frac{e^{ht}}{ht}=1] where $h$ is the topological entropy of the geodesic flow. In the appendix, we also show that the unique measure of maximal entropy of the geodesic flow has the Bernoulli property.
We study the existence of closed geodesics on compact Riemannian orbifolds, and on noncompact Riemannian manifolds in the presence of a cocompact, isometric group action. We show that every noncontractible Riemannian manifold which admits such an act ion, and every odd-dimensional, compact Riemannian orbifold has a nontrivial closed geodesic.
154 - Weisheng Wu , Fei Liu , Fang Wang 2018
In this article, we study the ergodicity of the geodesic flows on surfaces with no focal points. Let $M$ be a smooth connected and closed surface equipped with a $C^infty$ Riemannian metric $g$, whose genus $mathfrak{g} geq 2$. Suppose that $(M,g)$ h as no focal points. We prove that the geodesic flow on the unit tangent bundle of $M$ is ergodic with respect to the Liouville measure, under the assumption that the set of points on $M$ with negative curvature has at most finitely many connected components.
106 - Christian Lange 2017
We show that on every compact Riemannian 2-orbifold there exist infinitely many closed geodesics of positive length.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا