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Almost Periodic Hill's Equation and the Rings of Saturn

Avron, Joseph E. and Simon, Barry (1981) Almost Periodic Hill's Equation and the Rings of Saturn. Physical Review Letters, 46 (17). pp. 1166-1168. ISSN 0031-9007.

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Incommensurate perturbations of classical orbits lead to an almost periodic Hill's operator whose spectrum, we argue, is a Cantor set, but one with large Lebesgue measure. Applied to the rings of Saturn, this implies that the complex groove structure in the rings approximates a Cantor set. We also emphasize the possible relevance of the sun in producing "side gaps" which magnify the apparent gap size.

Item Type:Article
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Simon, Barry0000-0003-2561-8539
Additional Information:© 1981 American Physical Society. (Received 30 January 1981) We thank J. Moser and R. Johnson for telling us of their work before publication, A. Dekel, L. Yaffe, and particularly P. Goldreich for useful discussions and criticism, I. Mikolic-Torreira for writing a computer program for us, and F. Dyson and P. Lax for encouragement. We would also like to thank the S. Fairchild Visiting Scholar Program and the California Institute of Technology Mathematics Department for their hospitality. This research is supported in part by the National Science Foundation under Grant No. MCS-78-01885.
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
Issue or Number:17
Classification Code:PACS numbers: 95.10.Ce, 03.65.Db, 96.30.Mh
Record Number:CaltechAUTHORS:20180417-104513184
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85894
Deposited By: George Porter
Deposited On:17 Apr 2018 19:54
Last Modified:03 Oct 2019 19:37

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