Abstract
This paper deals with the dynamics of linear Hamiltonian systems which have almost periodic Hamiltonians and symplectic phase transitions over almost periodic lattices. By introducing some discrete skew-product dynamical systems based on certain joint hulls of Hamiltonians and lattices, it will be proved that such a system admits a well-defined rotation number, which gives a global, topological understanding on the motion of these systems in symplectic groups and manifolds of Lagrangian planes.
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M. Zhang was supported by the National Basic Research Program of China (Grant no. 2006CB805903), the Doctoral Fund of Ministry of Education of China (Grant no. 20090002110079), the National 111 Project of China (2007) and the Natural Science Foundation of China (Grant no. 10531010).
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Li, L., Zhang, M. Rotation Numbers of Linear Hamiltonian Systems with Phase Transitions over Almost Periodic Lattices. Lett Math Phys 100, 51–75 (2012). https://doi.org/10.1007/s11005-011-0475-z
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DOI: https://doi.org/10.1007/s11005-011-0475-z