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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 ...
Geodesics in Margulis spacetimes     Margulis spacetimes  Geodesics       font style='font-size:12px;'> 2015/9/29
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 ...
RECURRENT GEODESICS IN FLAT LORENTZ 3-MANIFOLDS     LORENTZ 3-MANIFOLDS  GEODESICS       font style='font-size:12px;'> 2015/9/29
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 ...
Infinite dimensional Morse theory for geodesics on Finsler manifolds.
Closed Geodesics and the Free Loop Space     Closed Geodesics  Free Loop Space       font style='font-size:12px;'> 2015/3/18
Closed Geodesics and the Free Loop Space.
Discrete Geodesics     Discrete Geodesics  coplanar       font style='font-size:12px;'> 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...
Aperiodic Sequences and Aperiodic Geodesics     Recurrence  Bernoulli-shift  Geodesic Flow  Flow-invariant Sets  Symbolic Dynamics       font style='font-size:12px;'> 2012/6/19
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...
Geodesics in the space of Kahler cone metrics     Geodesics  the space of Kahler cone metrics  Analysis of PDEs       font style='font-size:12px;'> 2012/5/9
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 ...
Morse Theory for Geodesics in Conical Manifolds      Geodesics  Morse Theory  Nonsmooth Analysis       font style='font-size:12px;'> 2011/2/28
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...
Geodesics in Conical Manifolds      Geodesics  Conical Manifolds        font style='font-size:12px;'> 2011/2/28
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 present the full set of analytical solutions of the geodesic equations of charged test particles in the Reissner-Nordstr¨om space-time in terms of the Weierstraß },  and  elliptic functions...

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