# The Fibonacci trace map as a complex dynamical system

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We discuss the trace map associated with the Fibonacci

quasicrystal. While the associated dynamical system has been studied heavily as a real dynamical system, it may also be regarded as a complex dynamical system. We study the stable set and give explicit bounds for the complex approximants. Quantum dynamical consequences of these results will be

explained. This is joint work with Serguei Tcheremchantsev.