# Analysis Seminar

## 5/4/2006

**Antonio Bove**

## University of Bologna

#### Hyperbolicity and the stability of the Hamilton system

##### We prove that the Cauchy Problem for a class of hyperbolic operators with double characteristics and whose simple null bicharacteristics have limit points on the set of double points is not well-posed in the $ C^{\infty} $ category, even though the usual Ivrii-Petkov conditions on the lower order terms are satisfied. According to the standard linear algebra classification these operators, at a double point, have fundamental matrices exhibiting a Jordan block of size 4.