SPECTRUM OF MULTIFRACTAL STRUCTURE OF A CIRCLE MAP WITH THE SILVER-MEAN WINDING NUMBER

The multifractal spectrum, the so-called f(alpha) spectrum, of dynamic al systems with quasiperiodic behavior, i.e., two incommensurate frequ encies, is studied via a discrete circle map with an irrational windin g number of the silver mean. It turns out that the f(alpha) spectrum f or the silver-mean winding number is almost the same as that for the g olden-mean winding number. This implies that the function f(alpha) is universal for the quasiperiodic transition to chaos, which is believed to be a generic property of f(alpha) spectra for all irrational windi ng numbers. Other properties such as the scaling laws and the distribu tion of dynamical variables are also studied and compared with those o f the golden-mean winding number.