Non-linear phenomena: background and history

Typical ferroresonance equations are found in many physical phenomena, such as meteorology (Edward Lorentz in 1963), Rayleigh-Benard thermal convection and the stability of the solar system (Jacques Laskar); their resolution has aroused the curiosity of many mathematicians [5][6] [7] . Similarities are also apparent in the waveforms described above.

It was Poincaré who laid the foundations for this in 1905, by studying non-integrable systems, such as several bodies in gravitational interaction, for which no temporal solution of the form F (t ) can be found; note in passing that the description on a plane of the evolution of non-linear systems is called a "Poincaré cut", the description...