The Power Matrix, coadjoint action and quadratic differentials |
| |
Authors: | Eric Schippers |
| |
Institution: | (1) Department of Mathematics Machray Hall, University of Manitoba, R3T 2N2 Winnipeg, Manitoba, Canada |
| |
Abstract: | The coefficients of a quadratic differential which is changing under the Loewner flow satisfy a well-known differential system
studied by Schiffer, Schaeffer and Spencer, and others. By work of Roth, this differential system can be interpreted as Hamilton's
equations. We apply the power matrix to interpret this differential system in terms of the coadjoint action of the matrix
group on the dual of its Lie algebra. As an application, we derive a set of integral invariants of Hamilton's equations which
is in a certain sense complete. In function theoretic terms, these are expressions in the coefficients of the quadratic differential
and Loewner map which are independent of the parameter in the Loewner flow. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|