Titlebook: Nonlinear Dynamics New Directions; Theoretical Aspects Hernán González-Aguilar,Edgardo Ugalde Book 2015 Springer International Publishing S

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On the Complexity of Some Geometrical Objects,eful when dealing with dynamical systems. We prove a new lower bound in the case of Cantor sets of the interval defined by analytic iterated function systems. We also give an upper bound for the ?-distortion complexity of invariant sets of uniformly hyperbolic dynamical systems.

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Fluctuations of Observables in Dynamical Systems: From Limit Theorems to Concentration Inequalitiesal observables and to get bounds rather than limit laws. We end up with two sections: one gathering various open problems, notably on random dynamical systems, coupled map lattices, and the so-called nonconventional ergodic averages; and another one giving pointers to the literature about moderate deviations, almost-sure invariance principle, etc.

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