A brief history of Kovalevskaya exponents and modern developments (Q1577148)

This is a survey of the history and modern applications of the Kovalevskaya exponents which are some sets of exponents associated with homogeneous solutions to nonlinear ordinary differential equations. First appeared in the famous paper by Kovalevskaya on the problem of integrability of the motion of a rigid body with a fixed point, they were reintroduced many times in relation to other problems and finally coined by this name by Harno Yoshida in 1983. In particular, the author examines their modern applications to integrability theory and nonlinear dynamics.