2 citations · 6 across the 7 of their papers we have counts for
5 papers · 1 filter
Buried Points in Julia Sets
Clinton P. Curry, John C. Mayer
We give an introduction to buried points in Julia sets and a list of questions about buried points, written to encourage aficionados of topology and dynamics to work on these quest…
Locally connected models for Julia sets
A. Blokh, C. Curry, L. Oversteegen
Let be a polynomial with a connected Julia set . We use continuum theory to show that it admits a \emph{finest monotone map $\ph$ onto a locally connected continuum $J_{\sim…
Recognizing indecomposable subcontinua of surfaces from their complements
Clinton P. Curry
We prove two theorems which allow one to recognize indecomposable subcontinua of closed surfaces without boundary. If is a subcontinuum of a closed surface , we call the com…
Any counterexample to Makienko's conjecture is an indecomposable continuum
Clinton P. Curry, John C. Mayer, Jonathan Meddaugh +1
Makienko's conjecture, a proposed addition to Sullivan's dictionary, can be stated as follows: The Julia set of a rational function R has buried points if and only if no component…
Characterizing indecomposable plane continua from their complements
Clinton P. Curry, John C. Mayer, E. D. Tymchatyn
We show that a plane continuum X is indecomposable iff X has a sequence (U_n) of not necessarily distinct complementary domains satisfying what we call the double-pass condition: I…