The Levels of Quasiperiodic Functions on the plane, Hamiltonian Systems and Topology
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.
- Publication:
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arXiv e-prints
- Pub Date:
- September 1999
- DOI:
- 10.48550/arXiv.math-ph/9909032
- arXiv:
- arXiv:math-ph/9909032
- Bibcode:
- 1999math.ph...9032N
- Keywords:
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- Mathematical Physics;
- Mathematics - Dynamical Systems;
- Mathematics - Mathematical Physics;
- 58F27 (Primary) 58F07 (Secondary)
- E-Print:
- LATEX2e, 4 pages