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Journal of Modern Dynamics (JMD)
 

Partial quasimorphisms and quasistates on cotangent bundles, and symplectic homogenization
Pages: 205 - 249, Issue 2, April 2012

doi:10.3934/jmd.2012.6.205      Abstract        References        Full text (375.7K)           Related Articles

Alexandra Monzner - Fakultät für Mathematik, TU Dortmund, Dortmund, Germany (email)
Nicolas Vichery - CMLS École Polytechnique, Palaiseau, France (email)
Frol Zapolsky - Mathematisches Institut der Ludwig-Maximilian-Universität, Munich, Germany (email)

1 A. Abbondandolo and M. Schwarz, Floer homology of cotangent bundles and the loop product, Geom. Topol., 14 (2010), 1569-1722.       
2 P. Albers, A Lagrangian Piunikhin-Salamon-Schwarz morphism and two comparison homomorphisms in Floer homology, Int. Math. Res. Not. IMRN, 2008, 56 pp.
3 A. Banyaga, Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique, Comment. Math. Helv., 53 (1978), 174-227.       
4 P. Bernard, Symplectic aspects of Mather theory, Duke Math. J., 136 (2007), 401-420.       
5 M. Brunella, On a theorem of Sikorav, Ens. Math. (2), 37 (1991), 83-87.       
6 M. Entov and L. Polterovich, Calabi quasimorphism and quantum homology, Int. Math. Res. Not., 2003, 1635-1676.       
7 M. Entov and L. Polterovich, Quasi-states and symplectic intersections, Comment. Math. Helv., 81 (2006), 75-99.       
8 M. Entov and L. Polterovich, Rigid subsets of symplectic manifolds, Compos. Math., 145 (2009), 773-826.       
9 M. Entov, L. Polterovich and F. Zapolsky, Quasi-morphisms and the Poisson bracket, Pure Appl. Math. Q., 3 (2007), part 1, 1037-1055.       
10 U. Frauenfelder and F. Schlenk, Hamiltonian dynamics on convex symplectic manifolds, Israel J. Math., 159 (2007), 1-56.       
11 R. Iturriaga and H. Sánchez-Morgado, A minimax selector for a class of Hamiltonians on cotangent bundles, Internat. J. Math., 11 (2000), 1147-1162.       
12 S. Lanzat, "Symplectic Quasi-Morphisms and Quasi-States for Noncompact Symplectic Manifolds," Ph. D. thesis, Technion - Israel Institute of Technology, Haifa.
13 S. Lanzat, Quasi-morphisms and symplectic quasi-states for convex symplectic manifolds, arXiv:1110.1555.
14 R. Leclercq, Spectral invariants in Lagrangian Floer theory, J. Mod. Dyn., 2 (2008), 249-286.       
15 J. N. Mather, Action minimizing invariant measures for positive-definite Lagrangian systems, Math. Z., 207 (1991), 169-207       
16 D. Milinković and Y.-G. Oh, Floer homology as the stable Morse homology, J. Korean Math. Soc., 34 (1997), 1065-1087.       
17 D. Milinković and Y.-G. Oh, Generating functions versus action functional. Stable Morse theory versus Floer theory, in "Geometry, Topology, and Dynamics" (Montreal, PQ, 1995), CRM Proc. Lecture Notes, 15, Amer. Math. Soc., Providence, RI, (1998), 107-125.       
18 A. Monzner and F. Zapolsky, A comparison of symplectic homogenization and Calabi quasi-states, J. Topol. Anal., 3 (2011), 243-263.       
19 Y.-G. Oh, Symplectic topology as the geometry of action functional. I. Relative Floer theory on the cotangent bundle, J. Diff. Geom., 46 (1997), 499-577.       
20 Y.-G. Oh, Symplectic topology as the geometry of action functional. II. Pants product and cohomological invariants, Comm. Anal. Geom., 7 (1999), 1-54.       
21 Y.-G. Oh, Construction of spectral invariants of Hamiltonian paths on closed symplectic manifolds, in "The Breadth of Symplectic and Poisson Geometry," Progr. Math., 232, Birkhäuser Boston, Boston, MA, (2005), 525-570.       
22 G. P. Paternain, L. Polterovich and K. F. Siburg, Boundary rigidity for Lagrangian submanifolds, non-removable intersections, and Aubry-Mather theory, Mosc. Math. J., 3 (2003), 593-619, 745.       
23 L. Polterovich, "The Geometry of the Group of Symplectic Diffeomorphisms," Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, 2001.       
24 L. Polterovich and K. F. Siburg, On the asymptotic geometry of area-preserving maps, Math. Res. Lett., 7 (2000), 233-243.       
25 P. Py, Quelques plats pour la métrique de Hofer, J. Reine Angew. Math., 620 (2008), 185-193.       
26 M. Schwarz, On the action spectrum for closed symplectically aspherical manifolds, Pacific J. Math., 193 (2000), 419-461.       
27 K. F. Siburg, Action-minimizing measures and the geometry of the Hamiltonian diffeomorphism group, Duke Math. J., 92 (1998), 295-319.       
28 K. F. Siburg, "The Principle of Least Action in Geometry and Dynamics," Lecture Notes in Mathematics, 1844, Springer-Verlag, Berlin, 2004.       
29 A. Sorrentino and C. Viterbo, Action minimizing properties and distances on the group of Hamiltonian diffeomorphisms, Geom. Topol., 14 (2010), 2383-2403.       
30 D. Théret, A complete proof of Viterbo's uniqueness theorem on generating functions, Topology Appl., 96 (1999), 249-266.       
31 Viterbo, C., Symplectic topology as the geometry of generating functions, Math. Ann. 292 (1992), no. 4, 685-710.       
32 C. Viterbo, Symplectic homogenization, arXiv:0801.0206.
33 F. Zapolsky, On the Lagrangian Hofer geometry in symplectically aspherical manifolds, arXiv:1201.0504.

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