Complex maps without invariant densities
Henk Bruin, Mike Todd
Abstract
We consider complex polynomials f(z) = z+c1 for ∈ 2 and c1 ∈ , and find some combinatorial types and values of such that there is no invariant probability measure equivalent to conformal measure on the Julia set. This holds for particular Fibonacci-like and Feigenbaum combinatorial types when sufficiently large and also for a class of `long-branched' maps of any critical order.
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