Nowhere-differentiable attractors

✍ Scribed by O. E. Rossler; C. Knudsen; J. L. Hudson; I. Tsuda

• Publisher: John Wiley and Sons
• Year: 1995
• Tongue: English
• Weight: 566 KB
• Volume: 10
• Category: Article
• ISSN: 0884-8173
• DOI: 10.1002/int.4550100104

✦ Synopsis

The notion of nowhere-differentiable attractors is illustrated with four prototype equations, that is, maps of invertible type. Four classes of nowhere-differentiable attractors can be distinguished so far: the (nongeneric) continuous-nonchaotic-nonfractal type; the (nongeneric) continuous-fractal type; the (generic) singular-continuous-fractal type; and the (generic) continuous-fractal-in-a-projection type. The history of all four classes is linked with the name of J. A. Yorke in different ways. Even though continuous fractal nowhere-differentiable attractors do not exist generically, the hypothesis that the fractal geometry of nature may be a consequence of the fact that nature is a differentiable dynamical system is strengthened. Attractors with nowhere-differentiable generic projections can mimic the whole richness of fractal pictures.