Periodic orbit quantization of the anisotropic Kepler problem

DOI10.1063/1.165899zbMath1055.81579OpenAlexW2053263669WikidataQ73464180 ScholiaQ73464180MaRDI QIDQ4526225

Freddy Bugge Christiansen, Predrag Cvitanović

Publication date: 16 January 2001

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.165899

Mathematics Subject Classification ID

Quantum chaos (81Q50) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) General quantum mechanics and problems of quantization (81S99) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Related Items (3)

Semiclassical mechanics of bound chaotic potentials ⋮ Zeta functions and periodic orbit theory: A review ⋮ Classical and semiclassical zeta functions in terms of transition probabilities

Cites Work

• The quantization of a classically ergodic system
• A rule for quantizing chaos?
• Recycling of strange sets: I. Cycle expansions
• Exponential instability of collision orbit in the anisotropic Kepler problem
• Unstable periodic orbits and semiclassical quantisation
• Existence of stable orbits in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">x</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">y</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>potential
• On dynamical zeta function
• Quantization of chaotic systems
• Applications of periodic‐orbit theory

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