Nevertheless, if the two intervals are disjoint, the Lyapunov exponent satisfies


If , then the Lyapunov exponent stays essentially constant
on each of the intervals.

On the other hand, if , then, on these exponentially small 
intervals, the Lyapunov exponent may vary by a constant.

E.g. assume  then  and, 


On the other hand, near the edges of , its value is given by


So, the Lyapunov exponent varies by the amount .