Talk:Zaslavskii map

mod 1

I just thought mod 1 was the remainder after dividing by 1, i.e. the fractional part, but looking at the modulo article it says the arguments must be integers. I ran across this map peripherally in some work I am doing, but I don't know how to resolve the discrepancy between these two articles. PAR 02:57, 16 Jun 2005 (UTC)

Hi Paul. I figured out that mod is the modulo. It just looked a bit out of place there. I mean, if I look at the formula,

$f_{\nu \mu \epsilon }(x,y)=(x_{n}+\nu (1+\mu y_{n})+\epsilon \nu \mu \cos(2\pi x_{n}){\textrm {mod}}\,1,e^{-r}(y_{n}+\epsilon \cos(2\pi x_{n})).\,$

there is modulo in the first term, and no modulo in the second. I wonder if would be good to write in the article the motivation for this map, and in particular, why the modulo is actually necessary. But maybe not, I have these questions because I never encountered this map before.

A second question I have is why on the left hand side one has x and y, but on the right hand side x_n and y_n. Is there a correspondence between these variables? Thanks. Oleg Alexandrov 03:15, 16 Jun 2005 (UTC)

Hi Oleg - I don't think there is any reason to have the modulo function on both sides, I mean, its just a function. I agree, it needs some background, but I ran across the map reading an article that was analyzing time series, trying to differentiate between chaos and random noise. (I have included that article in the references). It was using various maps as tests of the method, but only stated the mapping equation, nothing else. I have not read the Zaslavskii reference, so I really know nothing more about it than the statement of the formula. If I can find the Z reference, I will put in some more. PAR 11:18, 16 Jun 2005 (UTC)

P.S. - Check out MathWorld PAR 11:31, 16 Jun 2005 (UTC)