SCALING OF POTENTIAL FUNCTION DERIVED FROM PARAMETER RENORMALIZATION OF MAPS

A systematic way for deriving the parameter renormalization equation f or one-dimensional maps is presented and the critical behavior of peri odic-doubling is investigated. The estimates of accumulation points an d universal constants match the known values asymptotically when the o rder of potential grows large. The potential function derived from the parameter renormalization equation shows scaling in the parameter spa ce with the universal convergent rate at the accumulation point, but w ith a different size scaling factor from the Feigenbaum constant.