Existence of closed geodesics through a regular point on translation surfaces
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DOI: 10.1007/s00208-019-01897-2
Abstract: We show that on any translation surface, if a regular point is contained in some simple closed geodesic, then it is contained in infinitely many simple closed geodesics, whose directions are dense in $${\mathbb {RP}}^1$$… read more here.
Keywords: closed geodesics; simple closed; translation; translation surfaces ... See more keywords
Counting closed geodesics in strata
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DOI: 10.1007/s00222-018-0832-y
Abstract: We compute the asymptotic growth rate of the number $$N({{\mathcal {C}}}, R)$$N(C,R) of closed geodesics of length $$\le R$$≤R in a connected component $${{\mathcal {C}}}$$C of a stratum of quadratic differentials. We prove that, for… read more here.
Keywords: geodesics strata; number; counting closed; closed geodesics ... See more keywords
On class A Lorentzian 2-tori with poles I: closed geodesics pass through poles
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DOI: 10.1007/s00229-018-1067-3
Abstract: In this paper, by studying certain isometries on globally hyperbolic planes, we prove that if p is a timelike pole on a class A Lorentzian 2-torus, then there exists a closed timelike geodesic passing through… read more here.
Keywords: tori poles; class; lorentzian tori; closed geodesics ... See more keywords
Closed geodesics on geodesic spaces of curvature
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DOI: 10.1016/j.exmath.2018.12.001
Abstract: Abstract We show how to use classical methods to prove that a compact, connected, non-contractible geodesic space of curvature ∞ has at least one closed geodesic. read more here.
Keywords: geodesic spaces; geodesics geodesic; spaces curvature; closed geodesics ... See more keywords