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