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Action minimizing properties and distances on the group of Hamiltonian diffeomorphisms

Alfonso Sorrentino and Claude Viterbo

Geometry & Topology 14 (2010) 2383–2403
Bibliography
1 A Banyaga, Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique, Comment. Math. Helv. 53 (1978) 174 MR490874
2 P Bernard, Symplectic aspects of Mather theory, Duke Math. J. 136 (2007) 401 MR2309170
3 M Bialy, L Polterovich, Invariant tori and symplectic topology, from: "Sinaĭ’s Moscow Seminar on Dynamical Systems" (editors L A Bunimovich, B M Gurevich, Y B Pesin, N (translation)), Amer. Math. Soc. Transl. Ser. 2 171, Amer. Math. Soc. (1996) 23 MR1359090
4 E Calabi, On the group of automorphisms of a symplectic manifold, from: "Problems in analysis (Lectures at the Sympos. in honor of Salomon Bochner, Princeton Univ., 1969)" (editor R C Gunning), Princeton Univ. Press (1970) 1 MR0350776
5 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
6 X Cui, An example of convex Hamiltonian diffeomorphism where asymptotic distance from identity is strictly greater than the minimal action, J. Differential Equations 246 (2009) 998 MR2474583
7 I Ekeland, H Hofer, Symplectic topology and Hamiltonian dynamics, Math. Z. 200 (1989) 355 MR978597
8 M Entov, L Polterovich, Quasi-states and symplectic intersections, Comment. Math. Helv. 81 (2006) 75 MR2208798
9 A Fathi, The Weak KAM theorem in Lagrangian dynamics, Preliminary version number 10 (2009)
10 H Hofer, On the topological properties of symplectic maps, Proc. Roy. Soc. Edinburgh Sect. A 115 (1990) 25 MR1059642
11 V Humilière, Continuité en topologie symplectique, PhD thesis, École Polytechnique (2008)
12 V Humilière, On some completions of the space of Hamiltonian maps, Bull. Soc. Math. France 136 (2008) 373 MR2415347
13 R Iturriaga, H Sánchez-Morgado, A minimax selector for a class of Hamiltonians on cotangent bundles, Internat. J. Math. 11 (2000) 1147 MR1809305
14 J N Mather, Action minimizing invariant measures for positive definite Lagrangian systems, Math. Z. 207 (1991) 169 MR1109661
15 K F Siburg, Action-minimizing measures and the geometry of the Hamiltonian diffeomorphism group, Duke Math. J. 92 (1998) 295 MR1612789
16 J C Sikorav, Rigidité symplectique dans le cotangent de Tn, Duke Math. J. 59 (1989) 759 MR1046748
17 A Cannas da Silva, Lectures on symplectic geometry, 1764, Springer (2001) MR1853077
18 A Sorrentino, Lecture notes on Mather’s theory for Lagrangian systems arXiv:1011.0590
19 C Viterbo, Symplectic homogenization arXiv:0801.0206
20 C Viterbo, Symplectic topology as the geometry of generating functions, Math. Ann. 292 (1992) 685 MR1157321
21 C Viterbo, Symplectic topology and Hamilton–Jacobi equations, from: "Morse theoretic methods in nonlinear analysis and in symplectic topology" (editors P Biran, O Cornea, F Lalonde), NATO Sci. Ser. II Math. Phys. Chem. 217, Springer (2006) 439 MR2276957