Talk:Doubling map

Merge proposal

Should definitely be merged. —Preceding unsigned comment added by Maxlittle2007 (talk • contribs) 10:07, 5 August 2009 (UTC)[reply]

This map is already described at dyadic transformation. I propose that the contents of this article is merged into dyadic transformation, and replaced with a redirect. Gandalf61 (talk) 12:21, 24 June 2009 (UTC)[reply]

It seems that this map has one more name, which I didn't know. Thaks for pointing it. Of course it can be merged.

I'm not sure but for me it looks like family of functions with different domains ( unit circle, unit interval ) and then different features and names. Can it be noted ? --Adam majewski (talk) 14:02, 24 June 2009 (UTC)[reply]

I would not put much more work into this article – it is really just about one map going from the interval [0,1] to itself which is interesting because of its behaviour when one applies it repeatedly. As you noticed, it is not defined on the unit circle. Additionally, it does not make much sense to apply it to the nonnegative reals – the definitions would not be equivalent. IMO it is not continuous on the unit interval because there is a discontinuity at 1/2. What I would do is integrate the two additional names (“doubling map” and “sawtooth map” which are indeed used by some people) into the other article and then replace this page with a redirect. -- Momotaro (talk) 14:44, 25 June 2009 (UTC)[reply]

This map ( maps) is used in complex dynamics so for me it is important. I have tried to put her some explanations but things are more complicated then I have thought. (:-)). I would like to have comparison of various doubling maps :

angle doubling map
distance doubling map on unit interval
doubling map on unit circle
... and many others which I do not know.

"it does not make much sense to apply it to the nonnegative reals " Do you mean that it should be real numbers ?

--Adam majewski (talk) 16:33, 25 June 2009 (UTC)[reply]

I am not saying it is not important, in fact, by “interesting when applied repeatedly” I did mean the dynamic behaviour. However, if you're interested in complex dynamics, you should give a definition (and a reference for it in some book, preferably) for complex numbers. You see: The second definition only applies to numbers in [0,1], the first one could be used for arbitrary real numbers, or nonnegative real numbers if you like, but I wouldn't know what to do with a complex number. As for applying it to other real numbers, there is nothing more to see than if you just apply it to [0,1], because all of R is mapped to [0,1] in the first iteration, so the dynamical behaviour in [1,2] is just a repetition of the behaviour in [0,1]. Of course, as you stated, one gets the sawtooth wave then, but that's more interesting for functional analysis. -- Momotaro (talk) 17:13, 25 June 2009 (UTC)[reply]

Consensus in favour of merger, so I have merged and redirected to dyadic transformation. Gandalf61 (talk) 15:25, 2 September 2009 (UTC)[reply]