On Tue, 4 Jul 2006, Martin Peach wrote:
Mathieu Bouchard wrote:
On Mon, 3 Jul 2006, Chuckk Hubbard wrote:
On 7/3/06, padawan12 padawan12@obiwannabe.co.uk wrote:
I forgot, what's the name for a curve that oscillates (asymptotically?) around a value converging on it, in the purest mathspeak?
Got me. Curious if you find out.
I don't think that there's a name for such a sequence.
A limit cycle? http://mathworld.wolfram.com/LimitCycle.html
No, a LimitCycle not only doesn't (generally) have a single Limit (the concept exists for the case where an ordinary Limit is not enough), it also can apply to cases where values don't "oscillate" around the Limit points.
Padawan is talking about something that does always converge. E.g. he might be thinking about exp(t)*sin(t) or sin(t)/t, neither of which have a limit cycle bigger than 1 element, which means that they have a single limit, and then calling that a limit cycle doesn't imply anything about oscillations.
_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju | Freelance Digital Arts Engineer, Montréal QC Canada