Abstract For compact manifolds with infinite fundamental group we present sufficient topological or metric conditions ensuring the existence of two geometrically distinct closed geodesics. We also extend results about generic Riemannian metrics to Finsler metrics. show a bumpy theorem for and prove that $$C^4$$ C</mml:mi...

We present an approach for detecting multiword phrases in mathematical text corpora. The method used is based on characteristic features of mathematical terminology. It makes use of a software tool named Lingo which allows to identify words by means of previously defined dictionaries for specific word classes as adjectives, personal names or nouns. The detection of multiword groups is done algo...

We show that the co-rays to a ray in a complete non-compact Finsler manifold contain geodesic segments to upper level sets of Busemann functions. Moreover, we characterise the co-point set to a ray as the cut locus of such level sets. The structure theorem of the co-point set on a surface, namely that is a local tree, and other properties follow immediately from the known results about the cut ...

We show that certain mechanical systems, including a geodesic flow in any dimension plus a quasi-periodic perturbation by a potential, have orbits of unbounded energy. The assumptions we make in the case of geodesic flows are: a) The metric and the external perturbation are smooth enough. b) The geodesic flow has a hyperbolic periodic orbit such that its stable and unstable manifolds have a tra...

A Smarandache geometry is a geometry which has at least one Smarandachely denied axiom(1969), i.e., an axiom behaves in at least two different ways within the same space, i.e., validated and invalided, or only invalided but in multiple distinct ways and a Smarandache n-manifold is a nmanifold that support a Smarandache geometry. Iseri provided a construction for Smarandache 2-manifolds by equil...