New special functions solving nonlinear autonomous dynamical systems

Details New special functions solving nonlinear autonomous dynamical systems New special functions solving nonlinear autonomous dynamical systems

2009-10-14

arxiv.org/abs/0910.2584v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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.

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