Multidimensional Autonomous Differential System with Unit Measure of Instability and Massive Particular Stability

An example of nonone-dimensional autonomous differential system is constructed in which,on the one hand, all solutions starting in the exterior of the unit ball tend to zero as time tends toinfinity, and on the other hand, the relative measure of the initial conditions of the solutions thatbegin in a ball centered at zero and move away from it at a sufficient distance with increasing timebecomes arbitrarily close to unity as the ball radius tends to zero. The nonlinear systemconstructed in this paper also possesses the zero linear approximation along the zero solution.