Quasi periodic motions from Hipparchus to Kolmogorov (Q2568660)

The paper outlines the history of the evolution of the conception of quasi-periodic motions from antiquity till present. The definition of quasi-periodic motions is given in the contemporary mathematical terminology. The roots of the problem can be found in the Aristotelian ideas where motions are considered to be composed of circular uniform motions. The theories on motion of the Moon allow to estimate the differences between the theories of Ptolemy, Hipparchus and Copernic. Ptolemy's geometric correction to Hipparchus's lunar theory is illustrated on figure. Kepler made possible to reject the scheme of the Heavens presented in terms of deferents and epicycles in favor of motion on ellipses. After the discovery of the Kepler's laws the Newtonian theory of gravitation was soon formulated. The classical astronomy was based on Newtonian mechanics and the perturbation theories of Laplace, Lagrange and Poincaré confirmed that the motion of the bodies is quasi periodic. This allowed to construct the algorithms, leading to contemporary methods of analytical mechanics and the theory of chaos. The paper includes a list of 32 references.