Nonlinear Dynamics and Chaos

A variety of techniques including the Frobenius method of infinite power series could solve almost all linear DEs of physical interest. However, some very fundamental questions such as the stability of the solar system led to DEs that were not linear, and for such DEs no analytic (including series representation) solution existed. In the 1890s, Henri Poincare, the great French mathematician, took upon himself the task of gleaning as much information from the DEs describing the whole solar system as was possible. The result was the invention of one of the most powerful branches of mathematics (topology) and the realization that the qualitative analysis of (nonlinear) DEs could be very useful.