You said spiraling out to a bounded circle is unstable, but doesn't that still satisfy the epsilon-delta condition of stability? Or are there limits on epsilon?
The condition for stability states that for all epsilon>0 exists a delta>0 ... This condition would be violated for the case above since you can just take epsilon=r/2 (r radius of the circle). --Buzi 16:40, 6 October 2008 (PDT)