Using Computer Algebra in Problem of Localization of Invariant Compacts of Dynamical Systems

The application of a method of localization of invariant compact sets of an isolated dynamical system for the study of dynamical systems of high dimension is discussed. Methods of computer algebra are suggested for solving typical localization problems: calculation of derivatives, analysis of power of polynomial function, investigation of a quadratic function for the positive definition and so on. These methods are used for the study of the 5th order Lorentz system. A family of localizing sets of elliptic type is obtained.