New special functions solving nonlinear autonomous dynamical systems
Classical Analysis and ODEs
2009-10-15 v1 Combinatorics
Abstract
A general solution is found for a large class of time continuous autonomous nonlinear dynamical systems, the so-called quasi-polynomial systems. This solution is expressed in terms of a new type of special functions defined via their Taylor series. The coefficients of these Taylor series are generated by a tensor that generalizes the factorial function and has a combinatorial meaning. The existence of these functions raises the question of the relation between them and the chaotic behaviour of the solutions that may appear for the quasi-polynomial dynamical systems.
Cite
@article{arxiv.0910.2584,
title = {New special functions solving nonlinear autonomous dynamical systems},
author = {Leon Brenig},
journal= {arXiv preprint arXiv:0910.2584},
year = {2009}
}