A tentative history of conservative chaos

• Abstract

It is well known that what is called today the chaos theory has its roots in the works of Henri Poincaré related to the restricted three-body problem .The most important continuator is David Birkhoff who framed the collection of concepts introduced by Poincaré into a first draft of the nonlinear dynamical system theory. The next key step was produced in the early sixties with the seminal paper by Edward Lorenz about a reduced model for Rayleigh-Bénard convection. This model was dissipative and thus contributed to use Poincaré’s concepts in the context of chaotic attractor. Then the chaos-boom arose in the middle of the seventies with contributions as those of Otto E. Rössler. For a more complete history of dissipative chaos, see [1]. Both branches of chaos start with Poincaré’s results showing that the three-body problem is not integrable and that there is a homoclinic or heteroclinic tangle leading to aperiodic behavior. His continuator, George Birkhoff showed that many-body systems can often be solved analytically with a perturbation theory. This contributions of Kolmogorov, Möser, Arnol’d, Ford, Chirikov, Hénon, etc. are reviewed.

History of conservative chaos