I once came across a Wikipedia page describing a system where

[Apteronotus]

I once came across a Wikipedia page describing a system where indifferent of the initial starting position, at some final time t=T the system would always reach the same equilibrium position.

Does anyone know what the name of such a system is?

I recall there was an animation of 4 balls each starting at different heights on the same ramp at t=0 and at t=T the balls were always at the same height on the ramp.

 

[tiny-tim]

Hi Apteronotus!

I think that's an attractor …

see http://en.wikipedia.org/wiki/Attractor" ​

 

[chrisbaird]

It would have to be an attractor with some kind of damping, otherwise you would get oscillatory motion around the equilibrium point. You could also call it a potential minimum