Talk:Tent map

Name
Need to explain why it's called a "tent map."


 * In mathematics, the tent map is an iterated function, in the shape of a tent

That's not a good-enough explanation? linas 14:37, 25 October 2005 (UTC)


 * If you plot $$x_{n+1}$$ versus $$x_n$$, it has two linear sections which rise to meet at [1/2,&mu;/2] - it looks like a tent.

Are these equations correct?


x_{n+1}=\left\{ \begin{matrix} \mu x_n    & \mathrm{for} x_n \le \frac{1}{2} \\ \\ \mu (1-x_n) & \mathrm{for} \frac{1}{2} \le x_n. \end{matrix} \right. $$

If $$x_n = \frac{1}{2}$$, both values apply. Which is correct? ☢ Ҡieff⌇↯ 11:49, 4 February 2006 (UTC)


 * Yes, the function appears to have two values when $$x_n = \frac{1}{2}$$, but the values coincide - they are both $$\frac{\mu}{2}$$. However, I have changed the definition in the article to avoid confusion. Gandalf61 15:41, 4 February 2006 (UTC)

Plot
There really ought to be a picture of the defining function right at the beginning of the article.


 * Done. Gandalf61 12:23, 21 December 2006 (UTC)

Orbit?
What is an 'orbit'. The article just uses this term without explaining it. 09:37, 15 March 2013 (UTC) — Preceding unsigned comment added by 217.156.133.130 (talk)


 * See orbit (dynamics) and orbit (group theory). In this case, the orbit of a point is the set of images of that point under repeated iterations of the tent map. So the orbit of 0 is {0}, whereas the orbit of 1 is {1,0}. Periodic and eventually periodic points have finite orbits; non-periodic points have infinite orbits. Gandalf61 (talk) 12:42, 15 March 2013 (UTC)