By Virgil Snyder, Charles Herschel Sisam
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Extra resources for Analytic Geometry of Space
L EMMA 2. If the Ekeland–Hofer capacities and the volume capacity form a generating system for symplectic capacities on Ell2n , then c B 41 D 12 . 2 C "/ for every " > 0. P ROOF OF L EMMA 2. We can assume that all capacities are normalized. By assumption, there exists a sequence fi of homogeneous and monotone functions in the cNk and in cvol forming normalized capacities which pointwise converge to QUANTITATIVE SYMPLECTIC GEOMETRY 31 c B . As is easy to see, cNk E 14 ; 1 Ä cNk B 4 12 for all k, and cvol E 14 ; 1 D cvol B 4 12 .
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Eur. Math. Soc. 1, 87–107 (1999).  L. Polterovich, The geometry of the group of symplectic diffeomorphisms, Lectures in Mathematics ETH Z¨urich, Birkh¨auser, Basel, 2001.  P. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math. 31, 157–184 (1978).  P. Rabinowitz, Periodic solutions of a Hamiltonian system on a prescribed energy surface, J. Differential Equations 33, 336–352 (1979).  F. Schlenk, Symplectic embedding of ellipsoids, Israel J. of Math. 138, 215–252 (2003).
Analytic Geometry of Space by Virgil Snyder, Charles Herschel Sisam