Strange and chaotic attractors

Abstract

Abstract In the early 1970s, mathematicians David Ruelle and Floris Takens introduced the concept of the strange attractor to describe the phenomenon of turbulence (Ruelle and Takens, 1971; see also Ruelle, 1991). A strange attractor is a subset of points in the phase space that is fundamentally different to that of the objects belonging to ordinary Euclidean geometry; it is a geometric object characterized by a dimension that is not an integer number. The French mathematician of Polish origin Benoit Mandelbrot, also in the 1970s, coined the expression ‘fractal’ to indicate geometric objects whose dimension is not integer (Mandelbrot, 1975): strange attractors are fractal objects.