Frontiers of Mathematics in China >
S. V. Kovalevskaya system, its generalization and discretization
Received date: 07 Sep 2012
Accepted date: 07 Mar 2013
Published date: 01 Oct 2013
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We consider an integrable three-dimensional system of ordinary differential equations introduced by S. V. Kovalevskaya in a letter to G. Mittag-Leffler. We prove its isomorphism with the three-dimensional Euler top, and propose two integrable discretizations for it. Then we present an integrable generalization of the Kovalevskaya system, and study the problem of integrable discretization for this generalized system.
Key words: Birational map; integrable map; algebraically integrable system
Matteo PETRERA , Yuri B. SURIS . S. V. Kovalevskaya system, its generalization and discretization[J]. Frontiers of Mathematics in China, 2013 , 8(5) : 1047 -1065 . DOI: 10.1007/s11464-013-0305-y
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