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1. | School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, Tel-Aviv 69978 |
References:
[1] |
L. Buhovsky, The $2/3$-convergence rate for the Poisson bracket, Geom. and Funct. Analysis, 19 (2010), 1620-1649.
doi: 10.1007/s00039-010-0045-z. |
[2] |
L. Buhovsky, M. Entov and L. Polterovich, Poisson brackets and symplectic invariants, Selecta Mathematica, 18 (2012), 89-157.
doi: 10.1007/s00029-011-0068-9. |
[3] |
F. Cardin and C. Viterbo, Commuting Hamiltonians and Hamilton-Jacobi multi-time equations, Duke Math. J., 144 (2008), 235-284.
doi: 10.1215/00127094-2008-036. |
[4] |
M. Entov and L. Polterovich, Quasi-states and symplectic intersections, Comm. Math. Helv., 81 (2006), 75-99.
doi: 10.4171/CMH/43. |
[5] |
M. Entov and L. Polterovich, $C^0$-rigidity of Poisson brackets, in "Proceedings of the Joint Summer Research Conference on Symplectic Topology and Measure-Preserving Dynamical Systems" (eds. A. Fathi, Y.-G. Oh and C. Viterbo), Contemporary Mathematics, 512, AMS, Providence, RI, (2010), 25-32.
doi: 10.1090/conm/512. |
[6] |
M. Entov and L. Polterovich, $C^0$-rigidity of the double Poisson bracket, Int. Math. Res. Notices, (2009), 1134-1158. |
[7] |
M. Entov, L. Polterovich and D. Rosen, Poisson brackets, quasi-states and symplectic integrators, Discrete and Continuous Dynamical Systems, 28 (2010), 1455-1468.
doi: 10.3934/dcds.2010.28.1455. |
[8] |
M. Entov, L. Polterovich and F. Zapolsky, Quasi-morphisms and the Poisson bracket, Pure and Applied Math. Quarterly, 3 (2007), 1037-1055. |
[9] |
M. B. Hastings, Making almost commuting matrices commute, Comm. Math. Phys., 291 (2009), 321-345.
doi: 10.1007/s00220-009-0877-2. |
[10] |
C. Pearcy and A. Shields, Almost commuting matrices, J. Funct. Anal., 33 (1979), 332-338.
doi: 10.1016/0022-1236(79)90071-5. |
[11] |
L. Polterovich, Symplectic geometry of quantum noise, arXiv:1206.3707, (2012). |
[12] |
F. Zapolsky, Quasi-states and the Poisson bracket on surfaces, J. Mod. Dyn., 1 (2007), 465-475.
doi: 10.3934/jmd.2007.1.465. |
[13] |
F. Zapolsky, On almost Poisson commutativity in dimension two, Electron. Res. Announc. Math. Sci., 17 (2010), 155-160.
doi: 10.3934/era.2010.17.155. |
show all references
References:
[1] |
L. Buhovsky, The $2/3$-convergence rate for the Poisson bracket, Geom. and Funct. Analysis, 19 (2010), 1620-1649.
doi: 10.1007/s00039-010-0045-z. |
[2] |
L. Buhovsky, M. Entov and L. Polterovich, Poisson brackets and symplectic invariants, Selecta Mathematica, 18 (2012), 89-157.
doi: 10.1007/s00029-011-0068-9. |
[3] |
F. Cardin and C. Viterbo, Commuting Hamiltonians and Hamilton-Jacobi multi-time equations, Duke Math. J., 144 (2008), 235-284.
doi: 10.1215/00127094-2008-036. |
[4] |
M. Entov and L. Polterovich, Quasi-states and symplectic intersections, Comm. Math. Helv., 81 (2006), 75-99.
doi: 10.4171/CMH/43. |
[5] |
M. Entov and L. Polterovich, $C^0$-rigidity of Poisson brackets, in "Proceedings of the Joint Summer Research Conference on Symplectic Topology and Measure-Preserving Dynamical Systems" (eds. A. Fathi, Y.-G. Oh and C. Viterbo), Contemporary Mathematics, 512, AMS, Providence, RI, (2010), 25-32.
doi: 10.1090/conm/512. |
[6] |
M. Entov and L. Polterovich, $C^0$-rigidity of the double Poisson bracket, Int. Math. Res. Notices, (2009), 1134-1158. |
[7] |
M. Entov, L. Polterovich and D. Rosen, Poisson brackets, quasi-states and symplectic integrators, Discrete and Continuous Dynamical Systems, 28 (2010), 1455-1468.
doi: 10.3934/dcds.2010.28.1455. |
[8] |
M. Entov, L. Polterovich and F. Zapolsky, Quasi-morphisms and the Poisson bracket, Pure and Applied Math. Quarterly, 3 (2007), 1037-1055. |
[9] |
M. B. Hastings, Making almost commuting matrices commute, Comm. Math. Phys., 291 (2009), 321-345.
doi: 10.1007/s00220-009-0877-2. |
[10] |
C. Pearcy and A. Shields, Almost commuting matrices, J. Funct. Anal., 33 (1979), 332-338.
doi: 10.1016/0022-1236(79)90071-5. |
[11] |
L. Polterovich, Symplectic geometry of quantum noise, arXiv:1206.3707, (2012). |
[12] |
F. Zapolsky, Quasi-states and the Poisson bracket on surfaces, J. Mod. Dyn., 1 (2007), 465-475.
doi: 10.3934/jmd.2007.1.465. |
[13] |
F. Zapolsky, On almost Poisson commutativity in dimension two, Electron. Res. Announc. Math. Sci., 17 (2010), 155-160.
doi: 10.3934/era.2010.17.155. |
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