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ONE of the main goals in the development of theory of chaotic dynamicalsystem has been to make progress in understanding of turbulence. The attemptsto related turbulence to chaotic motion got strong impetus from the celebratedpaper by Ruelle and Takens . Considerable success has been achieved mainly inthe area: the onset of turbulence. For fully developed turbulence, manyquestions remain unanswered. The aim of this letter is to show that there aredynamical systems that are much simpler than the Navier-Stokes equations butthat can still have turbulent states and for which many concepts developed inthe theory of dynamical systems can be successfully applied. In this connectionwe advocate a broader use of the universal properties of a wide range ofisotropic turbulence phenomena. Even for the case of fully developedturbulence, which contains an extreme range of relevant length scales, it ispossible, by using the present model, to reproduce a surprising variety ofrelevant features, such as multifractal cascade, intermittency. This letterreverts to possible applications of the Navier-Stokes equations to studies ofthe nature of turbulence.

Logistic map and micro-structure of isotropic turbulent flow