A note on the limiting entry and return times distributions for induced maps

2012/08/30 by Haydn, Nicolai T A
#37A05 #37A25 #60E05 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1208.6059

Abstract

For ergodic measures we consider the return and entry times for a measure preserving transformation and its induced map on a positive measure subset. We then show that the limiting entry and return times distributions are the same for the induced maps as for the map on the entire system. The only assumptions needed are ergodicity and that the measures of the sets along which the limit is taken go to zero.

Related

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• Hitting-time Limits for some Exceptional Rare Events of Ergodic Maps
• A Survey of the Return Times Theorem
• Return- and hitting-time distributions of small sets in infinite measure preserving systems
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