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  • Lyusternik–Fet theorem - Wikipedia
    In mathematics, the Lyusternik–Fet theorem states that on every compact Riemannian manifold there exists a closed geodesic [1] It is named after Lazar Lyusternik and Abram Ilyich Fet, who published it in 1951
  • Closed geodesics on geodesic spaces of curvature lt;∞
    In 1951, Lyusternik and Fet showed that there exists at least one closed geodesic on every closed Riemannian manifold; see [7] The aim of this work is to prove the Lyusternik and Fet Theorem for geodesic spaces:
  • differential geometry - Example of compact Riemannian manifold with . . .
    The Lyusternik-Fet theorem states that every compact Riemannian manifold has at least one closed geodesic Are there any easy-to-construct1 examples of compact Riemannian manifolds for which it i
  • Lusternik Schnirelmann theory -
    On a closed surface of negative curvature every curve that is not null-homotopic can be deformed into a closed geodesic (Hadamard, 1898) On a simply connected compact surface there exist at least three closed geodesics without self-intersections (Lusternik and Schnirelmann, 1929) On a compact Riemannian manifold there exists at least one
  • Lyusternik–Fet theorem - HandWiki
    In mathematics, the Lyusternik–Fet theorem states that on every compact Riemannian manifold there exists a closed geodesic It is named after Lazar Lyusternik and Abram Ilyich Fet, who published it in 1951
  • Double pendulum motion (and Lyusternik-Fet Theorem)
    The discussion centers on the Lyusternik-Fet theorem, which asserts that for every pair of integers m and n, there exists a periodic motion on a 2-torus representing the configuration space of a double pendulum
  • arXiv:2207. 02557v1 [math. MG] 6 Jul 2022
    xposition of the Fet-Lyusternik result Another more modern expositio of the topic is given in ch 5 of [8] It is natural to ask whether the existence result for periodic geodesics applies to wider classes of spaces and whether th
  • Morse theory, closed geodesics, and the homology of free loop spaces
    In § 4 we give the proof of the famous Lyusternik-Fet theorem, and explain the principle of subordinated classes of Lyusternik-Schnirelmann, which allows to detect distinct critical levels
  • Periodic motion on a torus and Lyusternik-Fet Theorem
    I recently came across the Lyusternik-Fet theorem concerning closed geodesics on a compact manifold For simplicity of description, take the 2-torus, and imagine it represents the configuration space of a double pendulum





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