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,μ/2] - it looks like a tent.

Are these equations correct?

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

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)