The Imani Periodic Functions: Genesis and Preliminary Results

The Leah-Hamiltonian, $H(x,y)=y^2\mathrm{/}2+3x^{4\mathrm{/}3}\mathrm{/}4$, is introduced as a functional equation for $x(t)$ and $y(t)$. By means of a nonlinear transformation to new independent variables, we show that this functional equation has a special class of periodic solutions which we designate the Imani functions. The explicit construction of these functions is done such that they possess many of the general properties of the standard trigonometric cosine and sine functions. We conclude by providing a listing of a number of currently unresolved issues relating to the Imani functions.