Collapsed indecomposable continua in area preserving two-dimensional dynamical systems

While invariant indecomposable continua can occur in two dimensional area preserving dynamical systems, it is often the case that processes that would normally produce these continua instead produce a collapsed version of the continua because of the area preserving constraints. The collapsed continuum and the dynamics on it have a strong relationship to an indecomposable continuum in a related dynamical system. We also prove that the presence of a homoclinic point of a saddle point $p$ in such a system has a branch $W^{u+}(p)$ of its unstable manifold that is inaccessible from the complement of the closure of $W^{u+}(p)$.