A Probabilistic Approach to Chaos

Lecturer: Professor José Ferreira Alves, Porto University

The Theory of Dynamical Systems is an area of Mathematics dedicated to the study of systems whose configuration changes with the evolution of time, generally described by differential equations or transformations iterated in some space. It is known that deterministic systems, even those governed by simple evolutionary laws, can present chaotic behaviour, characterized by sensitivity to initial conditions, that is, a small perturbation of the initial state leads to an evolution very different from what would be expected for the system. Taking the Lorenz attractor as an example, we will illustrate the unpredictability of chaotic systems from a deterministic point of view (the popularised butterfly effect) and also give a perspective on how a probabilistic approach to chaotic systems can be particularly successful.

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