A survey on the Kovalevskaya exponents and their applications (Q2050916)

The article under review gives an extensive review on the Kovalevskaya exponents and the related applications, particularly in the integrability problems. More precisely, the authors review the previous results about Kovalevskaya exponents of quasi-homogeneous differential systems, of semi-quasi-homogeneous systems and of Hamiltonian system, the relationship between Kovalevskaya exponents and Darboux polynomials, Painlevé property. A large number of examples are given to illustrate results about the Kovalevskaya exponents.