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