hw2.ergd - Ergodic Theory MTG 6401 Ergodic HW Prof JLF King...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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 “
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Ask a homework question - tutors are online