Persistent Markov partitions for rational maps

Mary Rees (University of Liverpool)

Frank Adams Room 1, Alan Turing Building,

Markov partitions have been a major tool in dynamics  for at least fifty years. Persistent Markov partitions, that is, partitions that persist on some open subset of parameter space, have been used in Complex dynamics since the 1980's, starting with the use of the Yoccoz puzzle for quadratic polynomials, and branching out from that in the work of Roesch, Aspenberg-Yampolsky, Timorin and others. I will describe how to produce and use a persistent Markov partition in some other contexts within the parameter space of rational maps. The construction is related to a contstruction of Markov partitions for expanding diffeomorphisms published 35 years ago, but there are some surprising difficulties, which will be discussed.

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