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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 187, Number 1, Pages 139–154
DOI: https://doi.org/10.4213/tmf8986 (Mi tmf8986) 		 
Commensurability and Molchanov's hypothesis

M. B. Gubaidullin

Faculty of Mathematics and Information Technologies, Federal State Budget Educational Organization of Higher Professional Education Bashkir State University, Ufa, Russia
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DOI: https://doi.org/10.4213/tmf8986
Abstract: About half a century ago, A. M. Molchanov conjectured the existence of a resonance structure of the solar system, stating that as the solar system evolves, its planets inevitably drift to orbits for which the ratios of their orbital periods become close to ratios of relatively small natural numbers. In Molchanov's opinion, this resonance property is ensured by small dissipative forces. We offer another possible explanation of this phenomenon without taking dissipation into account.
Keywords: resonance, commensurability.
Received: 09.06.2015
Revised: 02.10.2015
English version:
Theoretical and Mathematical Physics, 2016, Volume 187, Issue 1, Pages 570–582
DOI: https://doi.org/10.1134/S0040577916040115
Bibliographic databases:
PACS: 96.12.De
MSC: 70E55
Language: Russian
Citation: M. B. Gubaidullin, “Commensurability and Molchanov's hypothesis”, TMF, 187:1 (2016), 139–154; Theoret. and Math. Phys., 187:1 (2016), 570–582
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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