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Invariant Measures is a category for books that study measures (often probabilities) that remain unchanged under a transformation, flow, or group action—core to ergodic theory, dynamical systems, and parts of probability and geometry. Titles range from introductions to measure-preserving systems and stationary distributions to advanced monographs on existence and construction of invariant measures, ergodicity, mixing, entropy, and stability. The collection bridges analysis, probability, and topology/geometry, featuring topics like Haar measure on groups, SRB and Gibbs measures, Markov chains and stochastic processes, and invariant distributions for differential equations. Applications span statistical physics, celestial mechanics, control, economics, and machine learning (e.g., MCMC). Geared to graduate students and researchers, these books provide rigorous foundations and practical methods for identifying, approximating, and exploiting invariant measures to understand long-term behavior of complex systems.

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