S. V. Kovalevskaya system, its generalization and discretization

Matteo PETRERA; Yuri B. SURIS

doi:10.1007/s11464-013-0305-y

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Front. Math. China ›› 2013, Vol. 8 ›› Issue (5) : 1047-1065. DOI: 10.1007/s11464-013-0305-y

RESEARCH ARTICLE

S. V. Kovalevskaya system, its generalization and discretization

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Abstract

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.

Keywords

Birational map / integrable map / algebraically integrable system

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Matteo PETRERA, Yuri B. SURIS. S. V. Kovalevskaya system, its generalization and discretization. Front Math Chin, 2013, 8(5): 1047‒1065 https://doi.org/10.1007/s11464-013-0305-y

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