Results 1 to 10 of about 135 (113)
Multiplicity of closed geodesics on Finsler spheres with irrationally elliptic closed geodesics [PDF]
Science China Mathematics, 2015 If all prime closed geodesics on $(S^n,F)$ with an irreversible Finsler metric $F$ are irrationally elliptic, there exist either exactly $2\left[\frac{n+1}{2}\right]$ or infinitely many distinct closed geodesics. As an application, we show the existence of three distinct closed geodesics on bumpy Finsler $(S^3,F)$ if any prime closed geodesic has non ...
Huagui Duan
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Topology, 2006 Improved version which takes into account the comments of the refree.
Guruprasad, K., Haefliger, André
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Multiple Closed Geodesics on Positively Curved Finsler Manifolds
Advanced Nonlinear Studies, 2019 In this paper, we prove that on every Finsler manifold (M,F){(M,F)} with reversibility λ and flag curvature K satisfying (λλ+1 ...
Wang Wei
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Closed Geodesics with Lipschitz Obstacle
Journal of Mathematical Analysis and Applications, 1999 It is considered a different kind of nonsmooth subset of \(\mathbb{R}^n\) with Lipschitz boundary. A new definition for geodesics on a general subset of \(\mathbb{R}^n\) is proposed and their basic property is showed. This definition is related to the nonsmooth critical point theory, presented below.
Marco Degiovanni
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Counting closed geodesics in moduli space
Journal of Modern Dynamics, 2011 We compute the asymptotics, as R tends to infinity, of the number of closed geodesics in Moduli space of length at most R, or equivalently the number of pseudo-Anosov elements of the mapping class group of translation length at most R.
Maryam Mirzakhani, Alex Eskin
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Connecting and Closed Geodesics of a Kropina Metric
Advanced Nonlinear Studies, 2021 We prove some results about existence of connecting and closed geodesics in a manifold endowed with a Kropina metric. These have applications to both null geodesics of spacetimes endowed with a null Killing vector field and Zermelo’s navigation problem ...
Caponio Erasmo +3 more
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On the equidistribution of closed geodesics and geodesic nets
Transactions of the American Mathematical Society, 2023 We show that given a closed n n -manifold
Li, Xinze, Staffa, Bruno
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Endpoint Geodesic Formulas on Graßmannians Applied to Interpolation Problems
Mathematics, 2023 Simple closed formulas for endpoint geodesics on Graßmann manifolds are presented. In addition to realizing the shortest distance between two points, geodesics are also essential tools to generate more sophisticated curves that solve higher order ...
Knut Hüper, Fátima Silva Leite
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Concentration of closed geodesics in the homology of modular curves
Forum of Mathematics, Sigma, 2023 We prove that the homology classes of closed geodesics associated to subgroups of narrow class groups of real quadratic fields concentrate around the Eisenstein line.
Asbjørn Christian Nordentoft
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The Global Attractor of the Allen-Cahn Equation on the Sphere
Frontiers in Applied Mathematics and Statistics, 2020 In this paper we study the attractor of a parabolic semiflow generated by a singularly perturbed PDE with a non-linear term given by a bistable potential, in an oval surface; the Allen-Cahn equation being a prototypical example.
David Medina, Pablo Padilla
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