Abstract:

Characteristic curves of homogeneous vector fields have in recent years experienced a kind of renaissance, due to interest in "eigenvectors of tensors" from various applications. In the seminar talk we relate the general concept for quasi-homogeneous vector fields to symmetry properties, and present and extend some existence results. Moreover an application to finding degree bounds for semi-invariants of polynomial vector fields will be discussed, as well as an application to determining the structure of the centralizer of a local analytic or formal vector field.
The talk reports on recent joint work with G. Gaeta, N. Kruff, J. Llibre, C. Pantazi and X. Zhang (in various combinations).

Slides of the talk.

Video of the talk.