Critical Points Properties of Ordinary Differential Equations as a Projection of Implicit Functions Using Spatio-temporal Taylor Expansion.

This contribution describes a new approach to formulation of ODE and PDE critical points using implicit formulation as t-variant scalar function using the Taylor expansion. A general condition for the critical points is derived and specified for t invariant case. It is expected, that the given new formulae lead to more reliable detection of critical points especially for large 3D fluid flow data acquisition, which enable high 3D vector compression and their representation using radial basis functions (RBF). In the case of vector field visualization, e.g. fluid flow, electromagnetic fields, etc., the critical points of ODE are critical for physical phenomena behavior.