A brief history of Kovalevskaya exponents and modern developments
The Kovalevskaya exponents are sets of exponents that can be associated with a given nonlinear vector field. They correspond to the Fuchs' indices of the linearized vector field around particular scale invariant solutions. They were used by S. Kovalevskaya to prove the single-valuedness of the...
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| Format: | Journal article |
| Language: | English |
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2000
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| Summary: | The Kovalevskaya exponents are sets of exponents that can be associated with a given nonlinear vector field. They correspond to the Fuchs' indices of the linearized vector field around particular scale invariant solutions. They were used by S. Kovalevskaya to prove the single-valuedness of the classical cases of integrability of the rigid body motion. In this paper, a history of the discovery and multiple re-discoveries of the Kovalevskaya exponents is given together with the modern use of Kovalevskaya exponents in integrability theory and nonlinear dynamics. © Regular and Chaotic Dynamics. |
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