Discrete Dynamical Systems as Models of Transport Phenomena: Large Deviations and Response

The role of fluctuations in dynamical systems has been widely studied in terms of fluctuation relations and response theory, in particular when it describes the response of a dynamical system to a perturbation, not limited to the usual linear response, which only applies to small perturbations. We investigate these issues treating in detail a given class of discrete time dynamical systems. This kind of toy models is very useful to understand the essential features of real transport phenomena and we study statistical properties of these systems and of their stochastic representation, including the behaviour of the cumulants of relevant observables.