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New limiting notions of the IP type in the enveloping semigroup

Published online by Cambridge University Press:  19 September 2008

Kamel N. Haddad
Kamel N. Haddad
Affiliation:
Mathematics Department, California State University at Bakersfield, 9001 Stockdale Hwy., Bakersfield, CA 93311, USA
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Abstract

An IP set in ℕ is a subset of ℕ which coincides with the set of finite sums taken from an infinite sequence in ℕ with not necessarily distinct terms. It has been established by H. Furstenberg and others that there is a rich connection between IP sets and idempotents in the enveloping semigroup E(X) of a compact metric dynamical system. Our aim in this paper is to further develop this program by considering special elements of E(X) with various IP properties.

Type
Survey Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 4 , August 1996 , pp. 719 - 733
Copyright
Copyright © Cambridge University Press 1996

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