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In this paper we investigate periodic orbits near a fixed point of a holomorphic twist map.
In this paper we investigate randomly perturbed orbits. If a dynamical system is hyperbolic one can keep random perturbations from accumulating into large deviations by making small corrections. We study the converse problem. This leads naturally to the notion of sustainable orbits.
We quantize the classical Henon map on $\mathbb R^2$, obtaining a unitary map on $L^2 (\mathbb R)$ whose dynamics we study, developing analogies to the classical dynamics.
We investigate complex dynamics in infinite dimensions. Such systems can be described via quasiconjugacies with finite dimensional systems. Natural examples can be found within the field of quantum chaos. We show that the dynamics localizes.
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