Volume 14, issue 3 (2010)

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

Volume 26
Issue 7, 2855–3306
Issue 6, 2405–2853
Issue 5, 1907–2404
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
Other MSP Journals
Symplectic topology of Mañé's critical values

Kai Cieliebak, Urs Frauenfelder and Gabriel P Paternain

Geometry & Topology 14 (2010) 1765–1870
1 A Abbondandolo, M Schwarz, Estimates and computations in Rabinowitz–Floer homology, J. Topol. Anal. 1 (2009) 307 MR2597650
2 R Abraham, J E Marsden, Foundations of mechanics, Benjamin/Cummings (1978) MR515141
3 D V Anosov, J G Sinaĭ, Some smooth ergodic systems, Uspehi Mat. Nauk 22 (1967) 107 MR0224771
4 V I Arnol’d, On some problems in symplectic topology, from: "Topology and geometry—Rohlin Seminar" (editor O Y Viro), Lecture Notes in Math. 1346, Springer (1988) 1 MR970068
5 V I Arnol’d, Mathematical methods of classical mechanics, Graduate Texts in Math. 60, Springer (1989) MR997295
6 M Audin, F Lalonde, L Polterovich, Symplectic rigidity: Lagrangian submanifolds, from: "Holomorphic curves in symplectic geometry" (editors M Audin, J Lafontaine), Progr. Math. 117, Birkhäuser (1994) 271 MR1274934
7 P Bernard, Symplectic aspects of Mather theory, Duke Math. J. 136 (2007) 401 MR2309170
8 K Burns, G P Paternain, Anosov magnetic flows, critical values and topological entropy, Nonlinearity 15 (2002) 281 MR1888853
9 L T Butler, An optical Hamiltonian and obstructions to integrability, Nonlinearity 19 (2006) 2123 MR2256655
10 L T Butler, G P Paternain, Magnetic flows on Sol-manifolds: dynamical and symplectic aspects, Comm. Math. Phys. 284 (2008) 187 MR2443302
11 C Camacho, A Lins Neto, Geometric theory of foliations, Birkhäuser (1985) MR824240
12 K Cieliebak, U A Frauenfelder, Morse homology on noncompact manifolds arXiv:0911.1805
13 K Cieliebak, U A Frauenfelder, A Floer homology for exact contact embeddings, Pacific J. Math. 239 (2009) 251 MR2461235
14 K Cieliebak, U A Frauenfelder, A Oancea, Rabinowitz Floer homology and symplectic homology, to appear in Ann. Sci. École Norm. Sup. arXiv:0903.0768
15 K Cieliebak, U A Frauenfelder, G P Paternain, Stability is not open arXiv:0908.2540
16 K Cieliebak, K Mohnke, Compactness for punctured holomorphic curves, J. Symplectic Geom. 3 (2005) 589 MR2235856
17 K Cieliebak, E Volkov, First steps in stable Hamiltonian topology arXiv:1003.5084
18 G Contreras, The Palais–Smale condition on contact type energy levels for convex Lagrangian systems, Calc. Var. Partial Differential Equations 27 (2006) 321 MR2260806
19 G Contreras, J Delgado, R Iturriaga, Lagrangian flows: the dynamics of globally minimizing orbits. II, Bol. Soc. Brasil. Mat. $($N.S.$)$ 28 (1997) 155 MR1479500
20 G Contreras, R Iturriaga, G P Paternain, M Paternain, Lagrangian graphs, minimizing measures and Mañé's critical values, Geom. Funct. Anal. 8 (1998) 788 MR1650090
21 G Contreras, L Macarini, G P Paternain, Periodic orbits for exact magnetic flows on surfaces, Int. Math. Res. Not. (2004) 361 MR2036336
22 N S Dairbekov, G P Paternain, On the cohomological equation of magnetic flows, Mat. Contemp. 34 (2008) 155 MR2588611
23 Y Eliashberg, A Givental, H Hofer, Introduction to symplectic field theory, from: "GAFA 2000 (Tel Aviv, 1999)" (editors N Alon, J Bourgain, A Connes, M Gromov, V Milman), Geom. Funct. Anal. Special Volume, Part II (2000) 560 MR1826267
24 A Fathi, E Maderna, Weak KAM theorem on non compact manifolds, Nonlinear Differential Equations Appl. 14 (2007) 1 MR2346451
25 R Feres, Geodesic flows on manifolds of negative curvature with smooth horospheric foliations, Ergodic Theory Dynam. Systems 11 (1991) 653 MR1145615
26 R Feres, A Katok, Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows, Ergodic Theory Dynam. Systems 9 (1989) 427 MR1016661
27 P Foulon, Feuilletages des sphères et dynamiques Nord-Sud, C. R. Acad. Sci. Paris Sér. I Math. 318 (1994) 1041 MR1281888
28 H Furstenberg, The unique ergodicity of the horocycle flow, from: "Recent advances in topological dynamics (Proc. Conf., Yale Univ., New Haven, Conn., 1972; in honor of Gustav Arnold Hedlund)" (editor A Beck), Lecture Notes in Math. 318, Springer (1973) 95 MR0393339
29 V L Ginzburg, On closed trajectories of a charge in a magnetic field. An application of symplectic geometry, from: "Contact and symplectic geometry (Cambridge, 1994)" (editor C B Thomas), Publ. Newton Inst. 8, Cambridge Univ. Press (1996) 131 MR1432462
30 V L Ginzburg, B Z Gürel, Periodic orbits of twisted geodesic flows and the Weinstein–Moser theorem, Comment. Math. Helv. 84 (2009) 865 MR2534483
31 V L Ginzburg, E Kerman, Periodic orbits in magnetic fields in dimensions greater than two, from: "Geometry and topology in dynamics (Winston–Salem, NC, 1998/San Antonio, TX, 1999)" (editors M Barge, K Kuperberg), Contemp. Math. 246, Amer. Math. Soc. (1999) 113 MR1732375
32 M Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
33 M Gromov, Kähler hyperbolicity and $L_2$-Hodge theory, J. Differential Geom. 33 (1991) 263 MR1085144
34 U Hamenstädt, Invariant two-forms for geodesic flows, Math. Ann. 301 (1995) 677 MR1326763
35 B Hasselblatt, Horospheric foliations and relative pinching, J. Differential Geom. 39 (1994) 57 MR1258914
36 B Hasselblatt, Regularity of the Anosov splitting and of horospheric foliations, Ergodic Theory Dynam. Systems 14 (1994) 645 MR1304137
37 M W Hirsch, C C Pugh, M Shub, Invariant manifolds, Lecture Notes in Math. 583, Springer (1977) MR0501173
38 H Hofer, K Wysocki, E Zehnder, A general Fredholm theory. I. A splicing-based differential geometry, J. Eur. Math. Soc. $($JEMS$)$ 9 (2007) 841 MR2341834
39 H Hofer, K Wysocki, E Zehnder, A general Fredholm theory. II. Implicit function theorems, Geom. Funct. Anal. 19 (2009) 206 MR2507223
40 H Hofer, E Zehnder, Symplectic invariants and Hamiltonian dynamics, Birkhäuser Advanced Texts: Basler Lehrbücher, Birkhäuser Verlag (1994) MR1306732
41 M Kanai, Differential-geometric studies on dynamics of geodesic and frame flows, Japan. J. Math. $($N.S.$)$ 19 (1993) 1 MR1231509
42 A Katok, B Hasselblatt, Introduction to the modern theory of dynamical systems, Ency. of Math. and its Appl. 54, Cambridge Univ. Press (1995) MR1326374
43 W Klingenberg, Riemannian geometry, de Gruyter Studies in Math. 1, de Gruyter (1982) MR666697
44 G Knieper, Hyperbolic dynamics and Riemannian geometry, from: "Handbook of dynamical systems, Vol. 1A" (editors B Hasselblatt, A Katok), North-Holland (2002) 453 MR1928523
45 F Laudenbach, J C Sikorav, Hamiltonian disjunction and limits of Lagrangian submanifolds, Internat. Math. Res. Notices (1994) MR1266111
46 G Lu, The Weinstein conjecture on some symplectic manifolds containing the holomorphic spheres, Kyushu J. Math. 52 (1998) 331 MR1645455
47 S Mac Lane, Categories for the working mathematician, Graduate Texts in Math. 5, Springer (1998) MR1712872
48 L Macarini, G P Paternain, On the stability of Mañé critical hypersurfaces, to appear in Calc. Var. Partial Diff. Equations arXiv:0910.5728
49 R Mañé, Lagrangian flows: the dynamics of globally minimizing orbits, Bol. Soc. Brasil. Mat. $($N.S.$)$ 28 (1997) 141 MR1479499
50 J N Mather, Action minimizing invariant measures for positive definite Lagrangian systems, Math. Z. 207 (1991) 169 MR1109661
51 D McDuff, Applications of convex integration to symplectic and contact geometry, Ann. Inst. Fourier (Grenoble) 37 (1987) 107 MR894563
52 D McDuff, D Salamon, Introduction to symplectic topology, Oxford Math. Monogr., The Clarendon Press, Oxford Univ. Press (1998) MR1698616
53 D McDuff, D Salamon, $J$–holomorphic curves and symplectic topology, Amer. Math. Soc. Coll. Publ. 52, Amer. Math. Soc. (2004) MR2045629
54 W Merry, Closed orbits of a charge in a weakly exact magnetic field, to appear in Pacific J. Math. arXiv:0906.1192
55 W Merry, On the Rabinowitz Floer homology of twisted cotangent bundles arXiv:1002.0162
56 W Merry, G P Paternain, Stability of Anosov Hamiltonian structures arXiv:0903.3969
57 K Nomizu, On the cohomology of compact homogeneous spaces of nilpotent Lie groups, Ann. of Math. $(2)$ 59 (1954) 531 MR0064057
58 S P Novikov, The Hamiltonian formalism and a multivalued analogue of Morse theory, Uspekhi Mat. Nauk 37 (1982) 3, 248 MR676612
59 W Parry, Synchronisation of canonical measures for hyperbolic attractors, Comm. Math. Phys. 106 (1986) 267 MR855312
60 G P Paternain, Magnetic rigidity of horocycle flows, Pacific J. Math. 225 (2006) 301 MR2233738
61 G P Paternain, M Paternain, Critical values of autonomous Lagrangian systems, Comment. Math. Helv. 72 (1997) 481 MR1476061
62 G P Paternain, L Polterovich, K F Siburg, Boundary rigidity for Lagrangian submanifolds, non-removable intersections, and Aubry–Mather theory, Mosc. Math. J. 3 (2003) 593, 745 MR2025275
63 L Polterovich, An obstacle to non-Lagrangian intersections, from: "The Floer memorial volume" (editors A Weinstein, E Zehnder), Progr. Math. 133, Birkhäuser (1995) 575 MR1362842
64 F Schlenk, Applications of Hofer's geometry to Hamiltonian dynamics, Comment. Math. Helv. 81 (2006) 105 MR2208800
65 P Scott, The geometries of $3$–manifolds, Bull. London Math. Soc. 15 (1983) 401 MR705527
66 D Sullivan, A foliation of geodesics is characterized by having no “tangent homologies”, J. Pure Appl. Algebra 13 (1978) 101 MR508734
67 C Viterbo, Symplectic homogeneization arXiv:0801.0206
68 C Viterbo, Functors and computations in Floer homology with applications. I, Geom. Funct. Anal. 9 (1999) 985 MR1726235
69 A W Wadsley, Geodesic foliations by circles, J. Differential Geometry 10 (1975) 541 MR0400257
70 A Weinstein, On the hypotheses of Rabinowitz' periodic orbit theorems, J. Differential Equations 33 (1979) 353 MR543704