ON COMPUTER-AIDED SOLVING DIFFERENTIAL EQUATIONS AND STUDYING STABILITY OF MARKETS

摘要

For any nonholonomic manifold, i.e., a manifold with nonintegrable distribution, we define an analog of the Riemann curvature tensor and refer to Grozman's package SuperLie with the help of which the tensor had been computed in several cases. Being an analog of the usual curvature tensor, this invariant characterizes (in)stability of any nonholonomic dynamical system, in particular, of markets. Similar invariants give criteria for formal integrability of differential equations whose symmetries are induced by contact transformations similar to Goldshmidt's criteria for formal integrability of differential equations whose symmetries are induced by point transformations. As a byproduct, we obtain an approximate solution of the equation whose integrability is under study.