홈 editorial content online
Volume 14 (2012)
No 1
Volume 13 (2011)
No 1
Volume 12 (2010)
No 1
Volume 11 (2009)
No 1, No 2
Volume 10 (2008)
No 1, No 2
Volume 9 (2006)
No 1, No 2
Volume 8 (2005)
No 1, No 2
Volume 7 (2004)
No 1, No 2
Volume 6 (2003)
No 1, No 2
Volume 5 (2002)
No 1, No 2
Volume 4 (2001)
No 1, No 2
Volume 3 (2000)
No 1
Volume 2 (1999)
No 1
Volume 1 (1998)
No 1
2008 International Workshop on Dynamical System and Realted Topics
(2008 / vol.10 / no.2)
Recurrence properties of interval exchange maps
Dong Han Kim
Pages. 105-109   



If an ergodic system has positive entropy, then the
Shannon-McMillan-Breiman theorem provides a relationship between the
entropy and the size of an atom of the iterated partition.
The system also has Ornstein-Weiss' first return time property,
which offers a method of computing the entropy via an orbit.
We consider irrational rotations and interval exchange maps
which are the typical model of zero entropy.
For almost every interval exchange map we show that the logarithm of
the recurrence time and hitting time to $r$-neighborhood normalized
by $-log r$ goes to 1.



1. Introduction
2. Irrational rotations
3. Interval exchange maps



37E05, 11J70