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===Classical Mechanics (CM)===

This difference in appearance has required very different scientific explanations.  Before the 20-th century, the physical laws of Isaac Newton were able to explain the motion of the planets and moons in the solar systems, but also solve many problems of everyday life.  This approach came to be called ''Classical Mechanics'' (CM).   It is based on the solution of ordinary differential equations.  They are able to explain what we now call [[chaos]], although finding the best methods for each case is not easy.  At the end of the 19-th century, Henri Poincare invented new treatments for chaotic systems, and his work was continued by many outstanding mathematicians and astronomers.  E.g. he used “[[Poincare Section|Surface of Section]]” where the same trajectory cuts through a fixed surface, over and over again, leaving a dot wherever it crossed.  In the simplest cases this leads to smooth curves, while chaos produces a wild scatter of isolated points.