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The 1996 Joint Spring Topology Conference and Southeast Dynamical Systems Conference
March 7-9, 1996
Ball State University
Muncie, IN, USA

Organizers
John Emert, Kerry Jones, Roger Nelson

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IP Cluster Points, Idempotents, and Recurrent Sequences
by
Aimee S. A. Johnson
Swarthmore College
Coauthors: Kamel N. Haddad (Swarthmore College)

We consider the dynamical system (M, S) where M is the orbit closure of a nonperiodic recurrent sequence of 0's and 1's (for example, the Morse sequence) and S is the shift map. The enveloping semigroup is E(M) = cl[Sn : n in Z], where the closure is taken in the topology of pointwise convergence. H. Furstenberg was the first to establish the existence of relationships between recurrence, IP sets, and idempotents in the enveloping semigroup, and the first author has proven that the closure of the set of idempotents coincides with the IP cluster points. In this paper the authors compute this set for (M, S) and shed light on other combinatorial properties of generalized Morse sequences.

Date received: January 26, 1996

Copyright © 1996 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 Mathematical Conference Abstracts. Document # caaa-13.