By Ballico E.
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Extra resources for A brill - noether theory for k-gonal nodal curves
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).
A brill - noether theory for k-gonal nodal curves by Ballico E.