Titlebook: Handbook of Dynamics and Probability; Peter Müller Book 2022 The Editor(s) (if applicable) and The Author(s), under exclusive license to S

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Introduction,el, and predict systems in quantitative sciences such as physics, biology, and economics. The time evolution of many of these systems is governed by dynamical laws that can be cast into a common mathematical form that makes them a dynamical system. Dynamical systems theory studies the properties of

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Ergodic Theoryissipative systems that do not conserve volume can. Volume is but a special kind of measure and studying the behavior of more general measures provides profound insights into dynamical systems, allowing to address questions such as whether points return to the set from which they originated, whether

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Probability Theory notions of conditional probabilities and statistical independence. The central concept of a random variable and its probability distribution and its expectation is introduced next. Moments, characteristic functions, generating functions, and escort distributions are various ways to describe the pro