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SUMMARY:The Shrinking Target Problem and Recurrence - Ayesha Bennett\, Uni
 versity of Cambridge
DTSTART:20250502T150000Z
DTEND:20250502T160000Z
UID:TALK229783@talks.cam.ac.uk
CONTACT:Adrian Dawid
DESCRIPTION:Full measure results for the most simple type of shrinking tar
 get and recurrence sets bring together two pillar stones in Ergodic theory
 \; the Ergodic Theorem and Poincare Recurrence. The study of both sets in 
 their full generality is motivated by results in Diophantine Approximation
 \, but has applications in many areas such as Transcendental Dynamics.\nTh
 is talk will discuss sufficient conditions on dynamical systems that lead 
 to a zero-one law for the shrinking target set. We also consider applicati
 ons of the zero-one law\; such as the frequency of strings of integers occ
 urring in the base b expansion of real numbers. Time permitting\, we will 
 end by briefly looking at why obtaining a zero-one law for the recurrence 
 set is more complex. \n\nThis talk does not assume any prior knowledge of 
 dynamical systems.
LOCATION:MR13
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