Abstract:
This is a short survey on the type numbers of closed geodesics, on applications of the Morse theory to proving the existence of closed geodesics and on the recent progress in applying variational methods to the periodic problem for Finsler and magnetic geodesics.
\Bibitem{Tai10}
\by I. A. Taimanov
\paper The type numbers of closed geodesics
\jour Regul. Chaotic Dyn.
\yr 2010
\vol 15
\issue 1
\pages 84--100
\mathnet{http://mi.mathnet.ru/rcd474}
\crossref{https://doi.org/10.1134/S1560354710010053}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2593232}
\zmath{https://zbmath.org/?q=an:1229.58015}
Linking options:
https://www.mathnet.ru/eng/rcd474
https://www.mathnet.ru/eng/rcd/v15/i1/p84
This publication is cited in the following 16 articles:
Hans-Bert Rademacher, “Simple closed geodesics in dimensions ⩾3”, J. Fixed Point Theory Appl., 26:1 (2024)
Hans-Bert Rademacher, “Two short closed geodesics on a sphere of odd dimension”, Calc. Var., 62:3 (2023)
Huagui Duan, Dong Xie, “Multiplicity of closed geodesics on bumpy Finsler manifolds with elliptic closed geodesics”, Journal of Functional Analysis, 284:8 (2023), 109861
Duan H.G., Liu H., “The Non-Contractibility of Closed Geodesics on Finsler Double-Struck Capital Rpn”, Acta. Math. Sin.-English Ser., 38:1 (2022), 1–21
Hui Liu, Yuchen Wang, “Multiplicity of non-contractible closed geodesics on Finsler compact space forms”, Calc. Var., 61:6 (2022)
Abreu M., Gutt J., Kang J., Macarini L., “Two Closed Orbits For Non-Degenerate Reeb Flows”, Math. Proc. Camb. Philos. Soc., 170:3 (2021), PII S0305004120000018, 625–660
Duan H., Long Y., Zhu Ch., “Index Iteration Theories For Periodic Orbits: Old and New”, Nonlinear Anal.-Theory Methods Appl., 201:SI (2020), 111999
Liu H., “The Optimal Lower Bound Estimation of the Number of Closed Geodesics on Finsler Compact Space Form S2N+1/Gamma”, Calc. Var. Partial Differ. Equ., 58:3 (2019), 107
Liu H., Long Y., Xiao Yu., “The Existence of Two Non-Contractible Closed Geodesics on Every Bumpy Finsler Compact Space Form”, Discret. Contin. Dyn. Syst., 38:8 (2018), 3803–3829
Hui Liu, “The Fadell–Rabinowitz index and multiplicity of non-contractible closed geodesics on Finsler RPn”, Journal of Differential Equations, 262:3 (2017), 2540
Marco Radeschi, Burkhard Wilking, “On the Berger conjecture for manifolds all of whose geodesics are closed”, Invent. math., 210:3 (2017), 911
Hui Liu, Yuming Xiao, “Resonance identity and multiplicity of non-contractible closed geodesics on Finsler RPn”, Advances in Mathematics, 318 (2017), 158
I. A. Taimanov, “The spaces of non-contractible closed curves in compact space forms”, Sb. Math., 207:10 (2016), 1458–1470
Alexis Michelat, Tristan Rivière, “A Viscosity method for the min-max construction of closed geodesics”, ESAIM: COCV, 22:4 (2016), 1282
Benjamin Schmidt, Craig Sutton, “Two remarks on the length spectrum of a Riemannian manifold”, Proc. Amer. Math. Soc., 139:11 (2011), 4113
I. A. Taimanov, “Periodic magnetic geodesics on almost every energy level via variational methods”, Regul. Chaotic Dyn., 15:4 (2010), 598–605
Citation in format AMSBIB
Contact us: