Abstract
We consider sticky sets in the phase space of circular mushroom billiards, which are referred to in physics literature as MUPOs (marginally unstable periodic orbits). An exact description of the set of parameters (widths of the mushrooms’ stems) without or with a finite set of MUPOs is given. It is shown that there exist a continuum of MUPOless parameters. We also estimate from above a number of MUPOs which exist for widths of the mushroom’s stem which correspond to rational numbers and present a simple approach for finding mushroom billiards without MUPOs.
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Acknowledgements
I am indebted to E. Altmann, C. Dettmann and O. Georgiou for very valuable comments on a draft of this paper.
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Bunimovich, L.A. Fine Structure of Sticky Sets in Mushroom Billiards. J Stat Phys 154, 421–431 (2014). https://doi.org/10.1007/s10955-013-0898-2
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DOI: https://doi.org/10.1007/s10955-013-0898-2