Re: the circle map

*To*: mathgroup at smc.vnet.net*Subject*: [mg52292] Re: the circle map*From*: Peter Pein <petsie at arcor.de>*Date*: Sun, 21 Nov 2004 07:23:28 -0500 (EST)*References*: <cneuml$qbc$1@smc.vnet.net> <cnn0rm$8pf$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Peter Valko wrote: > Roger, > Can you tell me why is it that in the following code of yours: > > Clear[x, y, n]; > a0 = 0.41209; > x[n_] := x[n] = Mod[-a0*x[n - 1] - y[n - 1], 1]; > y[n_] := y[n] = Mod[x[n - 1], 1] ; > x[0] = 0.7; > y[0] = .65; > a = Table[{x[n], y[n]}, {n, 0, 10000}]; > ListPlot[a, PlotRange -> All] ; > > we get a fractal-like pic, but changing to a0 = 0.41208 we do not? This behaviour is typical for chaotic systems. See for instance http://mathworld.wolfram.com/LogisticMap.html > (And why is that replacing Mod[-,1] by FractionalPart[-] in the above > code will not give the same phenomenon? (#1[-a0*0.7 - 0.65] & ) /@ { Mod[#1, 1] & , FractionalPart } {0.06153699999999995, -0.938463} > > Peter > > -- Peter Pein 10245 Berlin