Inverse limits of postcritically finite polynomials

We examine inverse limits of postcritically finite polynomials restricted to their Julia sets. We define the “trunk” of a Julia set, a forward-invariant set related to the Hubbard tree, and use it to show that the inverse limit always contains at least one indecomposable subcontinuum. We characterize when the inverse limit is indecomposable and also examine how the trunk behaves in the inverse limit.