Equation of motion from a geophysical data series

The method of global vector field reconstruction described by Gouesbet and Letellier (1994) is used for reconstruction of system of nonlinear differential equations in three dimensional space from one observable series. The scheme has been tested for Rossler equations, the possibility of noise has been taken into account, and then results obtained were applied for investigations of geomagnetic pulsations and sunspot numbers. Some curious results can be explained by analysis of self-intersections in space being reconstructed.