Volume 14, issue 1 (2014)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 21
Issue 4, 1595–2140
Issue 3, 1075–1593
Issue 2, 543–1074
Issue 1, 1–541

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
On the multiplicity of isometry-invariant geodesics on product manifolds

Marco Mazzucchelli

Algebraic & Geometric Topology 14 (2014) 135–156
Bibliography
1 V Bangert, Closed geodesics on complete surfaces, Math. Ann. 251 (1980) 83 MR583827
2 V Bangert, On the existence of closed geodesics on two-spheres, Internat. J. Math. 4 (1993) 1 MR1209957
3 V Bangert, N Hingston, Closed geodesics on manifolds with infinite abelian fundamental group, J. Differential Geom. 19 (1984) 277 MR755226
4 V Bangert, W Klingenberg, Homology generated by iterated closed geodesics, Topology 22 (1983) 379 MR715246
5 R Bott, On the iteration of closed geodesics and the Sturm intersection theory, Comm. Pure Appl. Math. 9 (1956) 171 MR0090730
6 J Franks, Geodesics on $S^2$ and periodic points of annulus homeomorphisms, Invent. Math. 108 (1992) 403 MR1161099
7 D Gromoll, W Meyer, Periodic geodesics on compact riemannian manifolds, J. Differential Geometry 3 (1969) 493 MR0264551
8 K Grove, Condition $(C)$ for the energy integral on certain path spaces and applications to the theory of geodesics, J. Differential Geometry 8 (1973) 207 MR0339270
9 K Grove, Isometry-invariant geodesics, Topology 13 (1974) 281 MR0370651
10 K Grove, M Tanaka, On the number of invariant closed geodesics, Bull. Amer. Math. Soc. 82 (1976) 497 MR0402810
11 K Grove, M Tanaka, On the number of invariant closed geodesics, Acta Math. 140 (1978) 33 MR0458476
12 N Hingston, Isometry-invariant geodesics on spheres, Duke Math. J. 57 (1988) 761 MR975120
13 N Hingston, On the growth of the number of closed geodesics on the two-sphere, Internat. Math. Res. Notices (1993) 253 MR1240637
14 Y Long, Multiple periodic points of the Poincaré map of Lagrangian systems on tori, Math. Z. 233 (2000) 443 MR1750931
15 Y Long, Index theory for symplectic paths with applications, Progress in Mathematics 207, Birkhäuser (2002) MR1898560
16 G Lu, The Conley conjecture for Hamiltonian systems on the cotangent bundle and its analogue for Lagrangian systems, J. Funct. Anal. 256 (2009) 2967 MR2502430
17 M Mazzucchelli, The Lagrangian Conley conjecture, Comment. Math. Helv. 86 (2011) 189 MR2745280
18 M Mazzucchelli, On the multiplicity of non-iterated periodic billiard trajectories, Pacific J. Math. 252 (2011) 181 MR2862147
19 M Mazzucchelli, Critical point theory for Lagrangian systems, Progress in Mathematics 293, Birkhäuser (2012) MR3015021
20 H B Rademacher, Metrics with only finitely many isometry invariant geodesics, Math. Ann. 284 (1989) 391 MR1001709
21 M Tanaka, On the existence of infinitely many isometry-invariant geodesics, J. Differential Geom. 17 (1982) 171 MR664493
22 M Vigué-Poirrier, D Sullivan, The homology theory of the closed geodesic problem, J. Differential Geometry 11 (1976) 633 MR0455028