Composant structure in inverse limits of Markov maps
by
David J. Ryden
Baylor University

This talk will begin with a survey of some recent results about the structure of composants in indecomposable metric continua - in particular, a theorem of Solecki according to which the composant equivalence relation of each indecomposable continuum is Borel bireducible with one of two canonical forms, E₀ and E₁.

For a map f of an interval I onto itself, the structure of composants in the inverse limit of {I, f} is related to the dynamics of f. We will discuss this relationship, especially as it is manifested in Markov maps, and give sufficient conditions for the composant equivalence relation to reduce to E₀. Finally, we will consider whether or not all Markov maps generate inverse limits of the simpler E₀ type.

Date received: February 28, 2003