Chaos and Boundary Values Problems of Dynamical Systems

The boundary values of problem that are 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: 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.