ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

9. Ordinary Differential Equations and Dynamical Systems

1991 MS Classification: 34 Pomazanov, Michael, Moscow State University, Russia About the structure of some typical singularities in implicit ordinary differential equations The system of implicit ordinary differential equations in form A(x, tẋ(t) = b(x, t) is studied by asymptotic methods in a domain close to the singular surface placed in a space of the vector x and parameter t, where the main determinant of matrix A(x, t) is vanished. The uniqueness theorem and existence theorem are fail for the singular solution x(t), if it intersect the singular surface. A limited number of the singular solutions through the singular point x_{0}, t_{0} passed was obtained for some conditions additional to the condition detA(x_{0}, t_{0}) = 0 . The various types of the singularities corresponds to these cases. They had been called the “turn”, the “intersection”, the “reflecting” and so on, and they appear in some physical applications. Reference: S. O. Alexeyev, and M. V. Pomazanov, Gauss-Bonnet Black Holes in Low Energy String Theory, Gravitation & Cosmology 3 1 (1997), 191-194