Nonlinear Dynamical Systems in Economics pp 67-101 | Cite as

# Ergodic Theory of Nonlinear Dynamics

## Abstract

This lectures provides an introduction to ergodic theory — the study of probabilistic properties of orbits generated by continuous- or discrete-time dynamical systems. It includes some elementary measure theory, together with the basic concepts and methods of ergodic theory, such as invariant, ergodic, natural probability measures, isomorphism and metric entropy. The notion of predictability of dynamical systems and the related definition of complex or chaotic dynamics are discussed and some basic results are applied to certain types of maps commonly used in applications. Finally, the lecture discusses Bernoulli systems, the relation between deterministic chaotic systems and stochastic processes, and the notion of *α*-congruence.

## Keywords

Invariant Measure Ergodic Theory Measurable Subset Topological Entropy Ergodic Measure## Preview

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