New minimal geodesics in the group of symplectic diffeomorphisms
type: Item
instance of: scholarly article
title: New minimal geodesics in the group of symplectic diffeomorphisms
zbMATH Open document ID: 0828.58028
DOI: 10.1007/BF01189394
author: Karl Friedrich Siburg
published in: Calculus of Variations and Partial Differential Equations
publication date: 1995-07-26T00:00:00Z
review text: The author computes the Hofer distance [\textit{H. Hofer}, Proc. R. Soc. Edinb., Sect. A 115, No. 1/2, 25-38 (1990; Zbl 0713.58004)] for a certain class of compactly supported symplectic diffeomorphisms of \(\mathbb{R}^{2n}\). They are mainly characterized by the condition that they can be generated by a Hamiltonian flow \(\varphi^t_H\) which possesses only constant \(T\)-periodic solutions for \(0 < T \leq 1\). It is also demonstrated that on this class Hofer's distance coincides with the one introduced by \textit{C. Viterbo} [Math. Ann. 292, No. 4, 685-710 (1992; Zbl 0780.58023)].
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 53D25
zbMATH DE Number: 778937
zbMATH Keywords: minimal geodesics
zbMATH Keywords: Hamiltonian flows
zbMATH Keywords: Hofer distance
zbMATH Keywords: symplectic diffeomorphisms
reviewed by: Dušan Repovš
MaRDI profile type: Publication
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cites work: Q3738287
full work available at URL: https://doi.org/10.1007/bf01189394
OpenAlex ID: W1991326932
description: scientific article; zbMATH DE number 778937