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We describe an interesting interplay between symbolic dynamics, the structure of the Mandelbrot set, permutations of periodic points achieved by analytic continuation, and Galois groups of certain polynomials. Internal addresses are a convenient and efficient way of describing the combinatorial...
We briefly survey the theory of thermodynamic formalism for uniformly hyperbolic systems, and then describe several recent approaches to the problem of extending this theory to non-uniform hyperbolicity. The first of these approaches involves Markov models such as Young towers, countable-state...
We consider parameters
for which 0 is preperiodic under the map
$$z\mapsto \lambda e^z$$
. Given k and l, let n(r) be the number of
$$0<|\lambda |\le r$$
such that 0 is mapped after k iterations to a...
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