@article{13fb884fb2ef4bc3baaee5208eecf29c,
title = "Closed geodesics on reversible Finsler 2-spheres",
abstract = "We extend two celebrated theorems on closed geodesics of Riemannian 2-spheres to the larger class of reversible Finsler 2-spheres: Lusternik–Schnirelmann{\textquoteright}s theorem asserting the existence of three simple closed geodesics, and Bangert–Franks–Hingston{\textquoteright}s theorem asserting the existence of infinitely many closed geodesics. To prove the first theorem, we employ the generalization of Grayson{\textquoteright}s curve shortening flow developed by Angenent–Oaks.",
keywords = "Closed geodesics, Lusternik–Schnirelmann theory, curve shortening flow, reversible Finsler metrics",
author = "{De Philippis}, Guido and Michele Marini and Marco Mazzucchelli and Stefan Suhr",
note = "Funding Information: We are grateful to Egor Shelukhin and Vuka{\v s}in Stojisavljevi{\'c} for pointing out a mistake in the original proof of Theorem . We are also grateful to the anonymous referee, who did a tremendous work with the first draft of the manuscript: in particular, for pointing out a mistake in the original proof of Theorem (iv), and for providing many valuable corrections and suggestions throughout the whole manuscript. Part of this work was carried out while Marco Mazzucchelli was visiting the Scuola Internazionale Superiore di Studi Avanzati (Trieste, Italy) in May 2018, and the Ruhr-Universit{\"a}t Bochum (Germany) in September–November 2019. We wish to thank both institutions for providing an excellent working environment. Marco Mazzucchelli and Stefan Suhr are supported by the SFB/TRR 191 “Symplectic Structures in Geometry, Algebra and Dynamics”, funded by the Deutsche Forschungsgemeinschaft. Funding Information: We are grateful to Egor Shelukhin and Vuka?in Stojisavljevi? for pointing out a mistake in the original proof of Theorem?5.4. We are also grateful to the anonymous referee, who did a tremendous work with the first draft of the manuscript: in particular, for pointing out a mistake in the original proof of Theorem?1.2 (iv), and for providing many valuable corrections and suggestions throughout the whole manuscript. Part of this work was carried out while Marco Mazzucchelli was visiting the Scuola Internazionale Superiore di Studi Avanzati (Trieste, Italy) in May 2018, and the Ruhr-Universit?t Bochum (Germany) in September?November 2019. We wish to thank both institutions for providing an excellent working environment. Marco Mazzucchelli and Stefan Suhr are supported by the SFB/TRR 191 ?Symplectic Structures in Geometry, Algebra and Dynamics?, funded by the Deutsche Forschungsgemeinschaft. Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",
year = "2022",
month = jun,
doi = "10.1007/s11784-022-00962-9",
language = "English (US)",
volume = "24",
journal = "Journal of Fixed Point Theory and Applications",
issn = "1661-7738",
publisher = "Springer Science + Business Media",
number = "2",
}