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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 19, Fasc. 2,
pages 407 - 412
 

A NON-ERGODIC PHENOMENON FOR SOME RANDOM DYNAMICAL SYSTEM

Andrzej Komisarski

Abstract: In [2] Jajte formulated the following question:

Let h (x) 0 and h (x) 1 be homeomorphisms of the interval [0,1] onto itself. Is it true that for any x (- [0,1] and almost any t (- (0,1) there exists a limit of a sequence

1 sum n -- ht1 o ...o hti(x) n i=1
for n --> oo , where t = (0,t1t2...)2 is a binary representation of t, i.e. t = sum ti2-i i>1 and ti (- (0,1)?

The answer is negative. We describe the set of condensation points of the sequence in some special cases.

1991 AMS Mathematics Subject Classification: Primary 60J1S; Secondary 26A18.

Key words and phrases: -

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