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AKP energy levels by a simple shooting scheme for a periodic orbit

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Abstract

We revisit the periodic orbit theory for the anisotropic Kepler problem, which is an important playground for quantum chaos. In order to explore the periodic orbit, Gutzwiller devised an iteration scheme which computes the Fourier coefficients of the orbit iteratively. Here we note, in a nutshell, that all one needs is the primary periodic orbit. We propose an alternative scheme taking into account the symmetry of the target trajectory and the scaling property of the AKP equation of motion. We show that a simple shooting scheme gives the final periodic orbit almost immediately.

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Authors and Affiliations

  1. Department of Physics, School of Science and Technology, Meiji University, 1-1-1 Higashimita, Tama, Kawasaki, Kanagawa, 214-8571, Japan

    Kazuhiro Kubo & Tokuzo Shimada

Authors
  1. Kazuhiro Kubo
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  2. Tokuzo Shimada
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Corresponding author

Correspondence to Tokuzo Shimada.

Additional information

This work was presented in part and was awarded the Best Paper Award at the 14th International Symposium on Artificial Life and Robotics, Oita, Japan, February 5–7, 2009

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Cite this article

Kubo, K., Shimada, T. AKP energy levels by a simple shooting scheme for a periodic orbit. Artif Life Robotics 14, 557–561 (2009). https://doi.org/10.1007/s10015-009-0743-5

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  • DOI: https://doi.org/10.1007/s10015-009-0743-5

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