New minimal geodesics in the group of symplectic diffeomorphisms
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)].
scientific article; zbMATH DE number 778937