Circle-like continua which are inverse limits on intervals
by
W. T. Ingram
University of Missouri - Rolla

We consider inverse limits on circles using weakly confluent, inessential bonding maps. The inverse limit of such a system is an indecomposable, chainable continuum. In an attempt to understand which chainable continua occur as the inverse limit of such a system, we consider a specific parameterized family of maps of [0, 1] onot [0, 1]. The graph of a typical member of this family is piecewise linear with each piece having slope 4 or -4, starting from the point (0, t) with positive slope and changing slope only at the top or bottom of the square. In this family, for each positive integer n, we find choices of the parameter t which produce a periodic orbit (or orbits) for 0 of period n, and the inverse limit at such a parameter value is an n-endpoint chainable continuum.

Date received: February 15, 2000