| Contents |
| According to Poincare, the Newtonian three-body problem admits no other first integrals in addition to those we know within a class of algebraic functions. In this lecture we will prove that the critical Hamilton-Jacobi equation admits no smooth homogeneous solutions. As we shall see, this result quite obstructs the possibility of smooth complete integrability of the problem in the sense of Liouville. |
|