A brief history of Kovalevskaya exponents and modern developments

Journal article

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.

Authors: Goriely, A

• Journal: Regular and Chaotic Dynamics
• Volume: 5
• Issue: 1
• Pages: 3-15
• Publication date: 2000-01-01
• DOI: 10.1070/RD2000v005n01ABEH000120
• EISSN: 1468-4845
• ISSN: 1560-3547
• Language: English