✦ LIBER ✦
An Exponential Formula for Polynomial Vector Fields: II. Lie Series, Exponential Substituition, and Rooted Trees
✍ Scribed by Rudolf Winkel
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 413 KB
- Volume
- 147
- Category
- Article
- ISSN
- 0001-8708
No coin nor oath required. For personal study only.
✦ Synopsis
Gro bner's Lie Series and the Exponential Formula provide different explicit formulas for the flow generated by a finite-dimensional polynomial vector field. The present paper gives (1) a generalization of the Lie series in case of non-commuting variables called Exponential Substituition, (2) a structural understanding of the three formulas and their mutual relationships in terms of rooted trees, and (3) as a byproduct new results on the enumeration, coding, and statistics of different kinds of rooted trees.