Periodic orbit theory in classical and quantum mechanics. (English) Zbl 1055.37514
This article is an introduction to the special issue of Chaos dedicated to the periodic orbit theory of the classical and quantum mechanics of classically chaotic dynamical systems.
MSC:
| 37-02 | Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory |
| 37C25 | Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics |
| 37A30 | Ergodic theorems, spectral theory, Markov operators |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 81Q50 | Quantum chaos |
| 37C30 | Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. |
References:
| [1] | DOI: 10.1090/S0002-9904-1967-11798-1 · Zbl 0202.55202 · doi:10.1090/S0002-9904-1967-11798-1 |
| [2] | DOI: 10.1063/1.1665328 · doi:10.1063/1.1665328 |
| [3] | DOI: 10.1063/1.1665328 · doi:10.1063/1.1665328 |
| [4] | DOI: 10.1063/1.1665328 · doi:10.1063/1.1665328 |
| [5] | Selberg A., J. Ind. Math. Soc. 20 pp 47– (1956) |
| [6] | DOI: 10.1002/cpa.3160250302 · doi:10.1002/cpa.3160250302 |
| [7] | DOI: 10.1002/cpa.3160250302 · doi:10.1002/cpa.3160250302 |
| [8] | DOI: 10.1103/PhysRevLett.61.2729 · doi:10.1103/PhysRevLett.61.2729 |
| [9] | DOI: 10.1088/0951-7715/3/2/005 · Zbl 0702.58064 · doi:10.1088/0951-7715/3/2/005 |
| [10] | DOI: 10.1103/PhysRevLett.63.823 · doi:10.1103/PhysRevLett.63.823 |
| [11] | DOI: 10.1088/0951-7715/3/2/006 · doi:10.1088/0951-7715/3/2/006 |
| [12] | Berry M. V., J. Phys. A 23 pp 4839– (1990) · Zbl 0715.58043 · doi:10.1088/0305-4470/23/21/024 |
| [13] | Christiansen F., Phys. Rev. Lett. 65 pp 2087– (1990) · Zbl 1050.37505 · doi:10.1103/PhysRevLett.65.2087 |
| [14] | Christiansen F., J. Phys. A 23 pp 713L– (1990) · Zbl 1050.37505 · doi:10.1103/PhysRevLett.65.2087 |
| [15] | DOI: 10.1103/PhysRevLett.65.2837 · Zbl 1050.70523 · doi:10.1103/PhysRevLett.65.2837 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
