The shift dynamics - indecomposable continua connection
by
Judy Kennedy
University of Delaware

For F a homeomorphism on a compact, locally connected, separable metric space having an invariant isolated set A such that F restricted to A factors over the shift on M-symbols, we prove, with the addition of mild conditions, that A is contained in an invariant continuum K which (1) is the closure of the entrainment set of A, (2) of which the boundary L is an invariant indecomposable continuum, and (3) is such that F restricted to K factors over a homeomorphism on an indecomposable continuum K'. Continua admitting homeomorphisms which factor over homeomorphisms on indecomposable continua are ``indecomposable-like'' in many respects, as are those whose boundaries are indecomposable. Indecomposability seems (roughly) to be the way a locally connected space makes the transition from shift dynamics to the ``rest'' of the space.

Date received: June 16, 2002