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In this talk, we give a proof of the conjecture of Hofer-Wysocki-Zehnder published in 2003 asserting that a smooth and autonomous Hamiltonian flow on R4 has either two or infinitely many simple period...
In this paper we give a combinatorial characterization of projections ofgeodesics in Euclidean buildings to Weyl chambers. We apply these results to the representation theory of complex reductive Lie ...
Let M3 be a Margulis spacetime whose associated complete hyperbolic surface 62 has a compact convex core. Generalizing the correspondence between closed geodesics on M3 and closed geodesics on 62 ...
We introduce the notion of recurrent geodesic rays in a complete °at Lorentz 3-manifold. We completely classify the dynamical behavior of geodesics in cyclic quotients, and apply this classiˉcation...
This paper introduces a novel approach for rapidly computing a very large number of geodesics on a smooth surface.The idea is to apply the recently developed phase flow method [L. Ying, E.J. Cande `s,...
This paper introduces a novel approach for rapidly computing a very large number of geodesics on a smooth surface. The idea is to apply the recently developed phase flow method [15], an efficient and ...
Closed Geodesics and the Free Loop Space.
Discrete Geodesics     Discrete Geodesics  coplanar       2014/10/30
Inside a triangle, the geodesic path is a line segment • When crossing an edge, the geodesic path is also a line segment if we unfold one triangle such that the two adjacent triangles are copla...
We introduce a quantitative condition on orbits of dynamical systems which measures their aperiodicity. We show the existence of sequences in the Bernoulli-shift and geodesics on closed hyperbolic man...
In this paper, we prove the existence and uniqueness of the weak cone geodesics in the space of K\"ahler cone metrics by solving the singular, homogeneous complex Monge-Amp\`{e}re equation. As an appl...
In this note we show that in metric measure spaces satisfying the reduced curvature-dimension condition CD*(K,N) we always have geodesics in the Wasserstein space of probability measures that satisfy ...
The aim of this paper is to extend the Morse theory for geodesics to the conical manifolds. In a previous paper [15] we de ned these manifolds as submanifolds of Rn with a nite number of conical sing...
The aim of this paper is to extend the definition of geodesics to conical manifolds, defined as submanifolds of Rn with a finite number of singu-larities.
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 geo...

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