There is a natural connection between two types of recurrence law: hittingtimes to shrinking targets, and hitting times to a fixed target (usually seenas escape through a hole). We show that for systems which mix exponentiallyfast, one can move through a natural parameter space from one to the other. Onthe other hand, if the mixing is subexponential, there is a phase transitionbetween the hitting times law and the escape law.
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