In turbulent flows energy cascades from larger to smaller scales following the Kolmogorov -5/3 power law. An analytical picture of the process underlying cascades in fluids or in other systems is not known. Based on a well-known discrete map we show a procedure that generates an analytical structure that produces a cascade from which the energy scaling law for isotropic homogeneous turbulence can be calculated. It is done by finding a function that unveils a non-self-similar (possibly) multifractal ruling the cascade. The backbone underlying the cascade is formed by deterministic nested polynomials. These results show that turbulent cascade behaviour can be found in low dimensional nonlinear dynamics. Consequently, turbulent cascades are not only exclusive for fluids but may also be present in many other systems, such as neurological information processing and epidemic dynamics.
