Universal canonical forms for time-continuous dynamical systems

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Abstract
A natural embedding for most time-continuous systems is presented. A set of nonlinear transformations is shown to split the whole family of dynamical systems into equivalence classes. The degree of nonlinearity is not a relevant characteristic of these classes of ordinary differential equations (ODE’s). In each class there exist two particular simple canonical forms into which any such ODE can be cast. We show on an example how to use these canonical forms to find nontrivial integrability conditions.