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55,603
Closed Geodesics and . . .
, 2008
"... We consider algebraic geometrical properties of the integrable billiard on a quadric Q with elastic impacts along another quadric confocal to Q. These properties are in sharp contrast with those of the ellipsoidal Birkhoff billiards in R n. Namely, generic complex invariant manifolds are not Abelian ..."
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are not Abelian varieties, and the billiard map is no more algebraic. A Ponceletlike theorem for such system is known. We give explicit sufficient conditions both for closed geodesics and periodic billiard orbits on Q and discuss their relation with the elliptic KdV solutions and elliptic Calogero system.
Correlations for pairs of closed geodesics
 Invent. Math
"... Abstract. In this article we consider natural counting problems for closed geodesics on negatively curved surfaces. We present asymptotic estimates for pairs of closed geodesics, the differences of whose lengths lie in a prescribed family of shrinking intervals. Related pair correlation problems hav ..."
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Cited by 17 (2 self)
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Abstract. In this article we consider natural counting problems for closed geodesics on negatively curved surfaces. We present asymptotic estimates for pairs of closed geodesics, the differences of whose lengths lie in a prescribed family of shrinking intervals. Related pair correlation problems
CLOSED GEODESICS IN LORENTZIAN SURFACES
"... Abstract. We show that every closed Lorentzian surface contains at least two closed geodesics. Explicit examples show the optimality of this claim. Refining this result we relate the least number of closed geodesics to the causal structure of the surface and the homotopy type of the Lorentzian metri ..."
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Cited by 5 (1 self)
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Abstract. We show that every closed Lorentzian surface contains at least two closed geodesics. Explicit examples show the optimality of this claim. Refining this result we relate the least number of closed geodesics to the causal structure of the surface and the homotopy type of the Lorentzian
Closed geodesics on orbifolds of revolution
 Houston J. Math
"... Abstract. Using the theory of geodesics on surfaces of revolution, we show that any twodimensional orbifold of revolution homeomorphic to S2 must contain an infinite number of geometrically distinct closed geodesics. Since any such orbifold of revolution can be regarded as a topological twosphere ..."
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Cited by 1 (0 self)
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Abstract. Using the theory of geodesics on surfaces of revolution, we show that any twodimensional orbifold of revolution homeomorphic to S2 must contain an infinite number of geometrically distinct closed geodesics. Since any such orbifold of revolution can be regarded as a topological two
CLOSED GEODESICS ON INCOMPLETE SURFACES.
, 2003
"... Abstract. We consider the problem of finding embedded closed geodesics on the twosphere with an incomplete metric defined outside a point. Various techniques including curve shortening methods are used. 1. Introduction. The existence of closed geodesics on a Riemannian surface often depends only on ..."
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Cited by 2 (0 self)
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Abstract. We consider the problem of finding embedded closed geodesics on the twosphere with an incomplete metric defined outside a point. Various techniques including curve shortening methods are used. 1. Introduction. The existence of closed geodesics on a Riemannian surface often depends only
Simple closed geodesics and the study of Teichmüller
"... 3 Simple closed geodesics versus the set of closed geodesics...... 5 3.1 The nondensity of simple closed geodesics............ 5 ..."
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3 Simple closed geodesics versus the set of closed geodesics...... 5 3.1 The nondensity of simple closed geodesics............ 5
On Closed Geodesics on Ellipsoids
, 2005
"... Closed geodesic lines on an ellipsoid in ddimensional Euclidean space are considered. Explicit algebrogeometric condition for closedness of such a geodesic is given. The obtained condition is discussed in light of thetafunctions theory and compared with some recent related results. 1 ..."
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Closed geodesic lines on an ellipsoid in ddimensional Euclidean space are considered. Explicit algebrogeometric condition for closedness of such a geodesic is given. The obtained condition is discussed in light of thetafunctions theory and compared with some recent related results. 1
COUNTING CLOSED GEODESICS IN STRATA
"... Abstract. We compute the asymptotic growth rate of the number N(C, R) of closed geodesics of length ≤ R in a connected component C of a stratum of quadratic differentials. We prove that, for any 0 ≤ θ ≤ 1, the number of closed geodesics γ of length at most R such that γ spends at least θ–fraction of ..."
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Cited by 3 (2 self)
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Abstract. We compute the asymptotic growth rate of the number N(C, R) of closed geodesics of length ≤ R in a connected component C of a stratum of quadratic differentials. We prove that, for any 0 ≤ θ ≤ 1, the number of closed geodesics γ of length at most R such that γ spends at least θ
CLOSED GEODESICS ON ORBIFOLDS
, 2006
"... Abstract. In this paper, we try to generalize to the case of compact Riemannian orbifolds Q some classical results about the existence of closed geodesics of positive length on compact Riemannian manifolds M. We shall also consider the problem of the existence of infinitely many geometrically distin ..."
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Cited by 8 (0 self)
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Abstract. In this paper, we try to generalize to the case of compact Riemannian orbifolds Q some classical results about the existence of closed geodesics of positive length on compact Riemannian manifolds M. We shall also consider the problem of the existence of infinitely many geometrically
LOOP PRODUCTS AND CLOSED GEODESICS
"... Abstract. The critical points of the length function on the free loop space Λ(M) of a compact Riemannian manifold M are the closed geodesics on M. The length function gives a filtration of the homology of Λ(M) and we show that the ChasSullivan product Hi(Λ) × Hj(Λ) ∗ ✲ Hi+j−n(Λ) is compatible wi ..."
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Cited by 10 (1 self)
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Abstract. The critical points of the length function on the free loop space Λ(M) of a compact Riemannian manifold M are the closed geodesics on M. The length function gives a filtration of the homology of Λ(M) and we show that the ChasSullivan product Hi(Λ) × Hj(Λ) ∗ ✲ Hi+j−n(Λ) is compatible
Results 1  10
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55,603