Chaos and Boundary Values Problems of Mathematical Models of Nonautonomous Dynamical Systems

The boundary values of problem thatare determined from observations play a decisive role in solving any problem in mathematical models of dynamic systems.They lead to the search of answer to the following questions:From observations, is it possible to find such boundary values, which could become the guarantor of the existence of smooth or chaotic solutions of the problem?This paper presents estimates of variations calculated from numerous observations: border estimates of the variations of the gravitational constant of the solar system:;10/1011113yearGG(I)Border estimates of the variations of iovocentric coordinates of V satellite of Jupiter:;540)0(61,0,810)0(22,0СС(II)border estimates of the variations of drift motions of daily satellites’ major semi-axes for the points where they intersectwith the equator, vary withindaykmdaykm/2,4/2,4(III)border estimates of changes of daily satellites’ longitude vary within:dayday/.deg0045,0/.deg0053,0(IV)border estimates of the variations of the rotation period of the daily satellites vary within:day055,0053,0(V)Ratings (I)-(V) obtained from the analysis of sums of infinitesimal perturbations of range less than or equal to the errors of observation.When satisfying the boundary estimates (I) -(V) of Solar System, orbits of V satellite and daily satellites are stable. Once these conditions are violated, chaos creeps in the orbits of the Solar System, V satellites and daily satellites and the orbits become unstable.