IP properties of recurrent sequences
by
Kamel N. Haddad
California State University, Bakersfield

An IP cluster point in the enveloping semigroup of a dynamical system (X, T) is a function of f with the property that given a neighborhood U of f in the topology of pointwise convergence, { n in N : Tⁿ in U } contains an IP set. By an IP set we mean a subset of N which coincides with the set of finite sums taken from an infinite sequence of distinct elements of N. If I(X) denotes the set of IP cluster points and J(X) the set of idempotents in the enveloping semigroup, then [`J(X)] = I(X). We present a computation of I(X) and J(X) in the case where X is the orbit closure of a recurrent sequence (as defined by Keane in his 1968 paper ``Generalized Morse sequences") and T the full shift. The computation yields that for these dynamical systems, J(X) = I(X) and |I(X)| = 4.

Date received: March 3, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caak-15.