Post-critically finite polynomials in arithmetic dynamics

Author / Creator

Goksel, Vefa, author

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Summary

Arithmetic dynamics is an area that studies the arithmetic properties of points under repeated application (iteration) of various maps such as polynomials or rational functions. This thesis consist...

Arithmetic dynamics is an area that studies the arithmetic properties of points under repeated application (iteration) of various maps such as polynomials or rational functions. This thesis consists of results on two problems in arithmetic dynamics. Both problems that we will study in this thesis concern post-critically finite polynomials, which are often seen as dynamical analogs of elliptic curves with complex multiplication in classical arithmetic geometry. In the first part, we will prove a connection between certain post-critically finite polynomials and Markov processes. In the second part, we will study the irreducibility of so-called Misiurewicz polynomials, which naturally arise from investigating the orbits of certain post-critically finite polynomials.

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