Symplectic capacities in two dimensions (Q1313536)

First, the author desribes the notion of the so-called symplectic capacity, a new type of symplectic invariants discovered recently, and then computes the Hofer-Zehnder-capacity \(c_{\text{HZ}}\) which was defined by \textit{H. Hofer} and \textit{E. Zehnder} [Analysis, et cetera, Res. Pap. in Honor of J. Moser's 60th Birthd., 405-427 (1990; Zbl 0702.58021)] via periodic solutions of Hamiltonian systems on two-dimensional connected manifolds \(M\) with an area element \(\omega\). It is shown that \(c_{\text{HZ}}\) is just the area \(| \int_ M\omega|\). The special case of the real plane, where another type of capacities exists, is also treated.