Embedding the torus automorphisms to Hamiltonian flows (Q1600488)

The goal of this paper is to study Hamiltonian flows resulting from the restricted and unrestricted embedding into \(\mathbb{R}^2\) of the 2-torus automorphisms. The torus automorphism is just a stroboscopic view of the flows at integer multiples of a fixed period \(T\). The authors present the torus automorphism and its explicit solution. Moreover they discuss the unrestricted embedding of the torus automorphism on \(\mathbb{R}^2\) and the restricted embedding, and conclude the paper with some remarks on the geodesic flow on the Lobashevskij plane, integrability, embedding and quantization. This is a continuation of the preceding paper [ibid. 12, 2805-2814 (2001; Zbl 1022.81013)].