Statistical properties of actions of periodic orbits
| Autor: | Mitsusada M. Sano |
|---|---|
| Rok vydání: | 2000 |
| Předmět: |
Pure mathematics
SPECTRAL STATISTICS STRANGE SETS Applied Mathematics Numerical analysis Modulo Symbolic dynamics SAWTOOTH MAP General Physics and Astronomy Statistical and Nonlinear Physics Sawtooth wave QUANTIZED BAKERS TRANSFORMATION Quantum chaos symbols.namesake Classical mechanics SEMICLASSICAL QUANTIZATION symbols CAT MAPS Quantum statistical mechanics Hamiltonian (quantum mechanics) Quantum Mathematical Physics Mathematics |
| Zdroj: | Chaos: An Interdisciplinary Journal of Nonlinear Science. 10:195-210 |
| ISSN: | 1089-7682 1054-1500 |
| DOI: | 10.1063/1.166485 |
| Popis: | We investigate statistical properties of unstable periodic orbits, especially actions for two simple linear maps (p-adic Baker map and sawtooth map). The action of periodic orbits for both maps is written in terms of symbolic dynamics. As a result, the expression of action for both maps becomes a Hamiltonian of one-dimensional spin systems with the exponential-type pair interaction. Numerical work is done for enumerating periodic orbits. It is shown that after symmetry reduction, the dyadic Baker map is close to generic systems, and the p-adic Baker map and sawtooth map with noninteger K are also close to generic systems. For the dyadic Baker map, the trace of the quantum time-evolution operator is semiclassically evaluated by employing the method of Phys. Rev. E 49, R963 (1994). Finally, using the result of this and with a mathematical tool, it is shown that, indeed, the actions of the periodic orbits for the dyadic Baker map with symmetry reduction obey the uniform distribution modulo 1 asymptotically as the period goes to infinity. (c) 2000 American Institute of Physics. |
| Databáze: | OpenAIRE |
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