Some Historical Aspects of Nonlinear Dynamics: Possible Trends for the Future

Abstract

This paper does not pretend to present a comprehensive history of nonlinear dynamics. Its purpose is more modest and limited to some historical aspects of this topic. The first part of this paper deals with the early foundations of nonlinear dynamics (essentially the Poincaré and Lyapunov results). The succeeding sections cover the period 1910–1970 and describes the development and contributions of the theory, elaborated by Birkhoff, the Andronov school, and the Krylov–Bogoliubov school. After 1970, the development of new results in nonlinear dynamics has become "explosive". A part of these results is presented in a summarized form in this paper. The last section suggests some possible trends for future research.