A scheme of q-deformation of nonlinear maps is introduced. As a specific
example, a q-deformation procedure related to the Tsallis q-exponential
function is applied to the logistic map. Compared to the canonical logistic
map, the resulting family of q-logistic maps is shown to have a wider spectrum
of interesting behaviours, including the co-existence of attractors -- a
phenomenon rare in one dimensional maps.Comment: 17 pages, 19 figure