| Abstract |
This thesis considers several problems in complex dynamics of one and several complex variables. In this work, I focus on four different topics: dynamics of quasi-hyperbolic Henon maps, local random dynamical systems, dynamics on strongly convex domains and dynamical properties of the Ising model. Every chapter of the thesis is dedicated to one of the aforementioned topics, but the focus of the thesis is to show how hyperbolic methods and the study of semi-group actions, can be applied in these different settings. The results I obtain relies on this common machinery.
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