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Topology in chaotic scattering

Abstract

In chaotic scattering, an initially freely moving orbit (such as that of an atom or a star) enters a scattering region and evolves chaotically for a period of time before it escapes and returns to free motion1. We have looked at cases in which escape can occur in three or more distinct ways. Using a laboratory model, we demonstrate experimentally that the regions of state space (called basins) corresponding to different ways of escaping can have an interesting topological property that we call the Wada property, by which we mean that these regions of state space might be so convoluted that every point on the boundary of a basin is on the boundary of all basins2,3.

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Figure 1: The light-scattering system used in our laboratory model.
Figure 2: Photograph of the laboratory model of the scatterer described in Fig. 1.

References

  1. Ott, E. Chaos in Dynamical Systems 166-179 (Cambridge Univ. Press, 1993).

  2. Poon, L., Campos, J., Ott, E. & Grebogi, C. Int. J. Bifurc. Chaos 6, 251–265 (1996).

    Google Scholar 

  3. Nusse, H. E. & Yorke, J. A. Science 271, 1376–1380 (1996).

    ADS  MathSciNet  CAS  Article  Google Scholar 

  4. Kovàcs, Z. & Wiesenfeld, L. Phys. Rev. E 51, 5476–5494 (1995).

    Google Scholar 

  5. Boyd, P. T. & McMillian, S. L. W. Chaos 3, 507–523 (1993).

    ADS  Article  Google Scholar 

  6. Sommerer, J. C., Ku, H.-C. & Gilreath, H. E. Phys. Rev. Lett. 77, 5055–5058 (1996).

    Google Scholar 

  7. Baranger, H. U., Jalabert, R. A. & Stone, A. D. Chaos 3, 665–682 (1993).

    ADS  Article  Google Scholar 

  8. Chen, Q. & Ding, M. & Ott, E. Phys. Lett. A 115, 93–100 (1990).

    Google Scholar 

  9. Alligood, K., Sauer, T. D. & Yorke, J. A. Chaos—An Introduction to Dynamical Systems 432-439 (Springer, New York, 1997).

  10. Alexander, D. S. AHistory of Complex Dynamics 131, 141-142 (Vieweg, 1994).

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Sweet, D., Ott, E. & Yorke, J. Topology in chaotic scattering. Nature 399, 315–316 (1999). https://doi.org/10.1038/20573

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