The Dynamical Fine Structure of Iterated Cosine Maps and a Dimension Paradox

We discuss in detail the dynamics of maps z 7→ aez + be −z for which both critical orbits are strictly preperiodic. The points which converge to ∞ under iteration contain a set R consisting of uncountably many curves called “rays”, each connecting ∞ to a well-defined “landing point” in C, so that every point in C is either on a unique ray or the landing… CONTINUE READING