Symplectic capacities in two dimensions
type: Item
instance of: scholarly article
title: Symplectic capacities in two dimensions
zbMATH Open document ID: 0791.58043
DOI: 10.1007/BF02599306
author: Karl Friedrich Siburg
published in: Manuscripta Mathematica
publication date: 1994-07-14T00:00:00Z
full work available at URL: https://eudml.org/doc/155801
review text: 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.
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 492769
zbMATH Keywords: symplectic manifolds
zbMATH Keywords: symplectic capacity
zbMATH Keywords: symplectic invariants
reviewed by: Yuri E. Gliklikh
MaRDI profile type: Publication
cites work: On a partial differential equation involving the Jacobian determinant
cites work: Symplectic topology and Hamiltonian dynamics
cites work: Differential Topology
cites work: On the topological properties of symplectic maps
cites work: Q3480936
cites work: Q3780144
OpenAlex ID: W2070283049
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description: scientific article; zbMATH DE number 492769