The Levels of Quasiperiodic Functions on the plane, Hamiltonian Systems and Topology
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Publication:6470117
DOI10.1070/RM1999V054N05ABEH000212arXivmath-ph/9909032MaRDI QIDQ6470117
Publication date: 28 September 1999
Abstract: Topology of levels of the quasiperiodic functions with m=n+2 periods on the plane is studied. For the case of functions with m=4 periods full description is obtained for the open everywhere dense family of functions. This problem is equivalent to the study of Hamiltonian systems on the (n+2)-torus with constant rank 2 Poisson bracket. In the cases under investigation we proved that this system is topologically completely integrable in some natural sence where interesting integer-valued locally stable topological characteristics appear. The case of 3 periods has been extensively studied last years by the present author, Zorich, Dynnikov and Maltsev for the needs of solid state physics (Galvanomagnetic Phenomena in Normal Metals); The case of 4 periods might be useful for Quasicrystals.
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