Routes to chaos and turbulence. A computational introduction

Abstract

Abstract We propose to survey in this paper different routes to chaos arising in nonlinear dynamic systems emphasizing where appropriate the connection with the intriguing phenomenon of turbulence in a viscous fluid. The onset of turbulence displays, in particular, clear chaotic characteristics. On the other hand, fully developed turbulence cannot be analysed presently by chaos theory as it stands and demands an expansion of the basic theory to incorporate spatial dependencies. Here we shall refer only to the onset of turbulence. Our approach is essentially a computational exploration and illustration.