Hw2.ergd - Ergodic Theory MTG 6401 Ergodic HW Prof JLF King 20Nov2006 H1 Suppose(T X X is a bi-mpt and A is a a.e(measurable set such that T 1(A =

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Ergodic Theory MTG6401 Ergodic HW Prof. JLF King 20Nov2006 H1: Suppose ( T : X, X ) is a bi-mpt. and A is a ( measurable ) set such that T 1 ( A ) a.e = A . Prove that there exists a set B a.e = A so that B is pointwise invariant, i.e, T 1 ( B ) = B . H2: Let R = R α be an irrational rotation of the circle X := [ 0 , 1 ) . Partition the circle into two half-open intervals, say A := [ 0 , 1 3 ) and B := [ 1 3 , 1 ) . Given a point z X , let the forward name of z be the sequence ( s 0 ,s 1 ,s 2 ,... ) , where s n is the symbol “
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This note was uploaded on 01/26/2012 for the course MTG 6401 taught by Professor Staff during the Fall '09 term at University of Florida.

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