Periodic Orbits for Transcendental Hénon Maps

Abstract

This master thesis deals with periodic points of transcendental Hénon maps, a subject in complex dynamics. In particular, we investigate the existence of periodic points and the discreteness of the set of $k$-periodic points for certain values of $k$. The simplest case is $k=1$, the fixed points. We employ known results from the theory of entire functions to show that transcendental Hénon maps $(z,w)\mapsto (f(z)-\delta w,z)$, where $f$ has finite and non-integer-valued order, admit infinitely many fixed points. We also give a complete description for the existence of fixed points in the case $f$ is a general entire function. For values of $k$ greater than 1, it is of interest to determine when a $k$-periodic point $(z,w)$, fails to be an $m$-periodic point for all $m