Turbulent diffusion for the radial twist map

An analytical tool is given to study the statistical properties of the radial twist map, X_n+1 = X_n + α(Y_n+1) and Y_n+1 = Y_n + Af (X_n), with arbitrary rotation number α(Y) and arbitrary periodic force f(X). The case for which f(X) = sin 2 πX and with arbitrary α is treated in the region of large A. The turbulent diffusion coefficient D for the chaotic orbit relaxes as $\text{t}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ to $\text{A}{}^2\text{4}$, except for the case of the standard map, where the eventual value of D is different from $\text{A}{}^2\text{4}$.