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By connecting dynamical systems and number theory, this graduate textbook on ergodic theory acts as an introduction to a highly active area of mathematics, where a variety of strands of research open up. The text explores various concepts in infinite ergodic theory, always using continued fractions and other number-theoretic dynamical systems as illustrative examples. Contents:PrefaceMathematical symbolsNumber-theoretical dynamical systemsBasic ergodic theoryRenewal theory and α-sum-level setsInfinite ergodic theoryApplications of infinite ergodic theoryBibliographyIndex

Ergodic theory. --- Topological dynamics. --- Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Dynamics, Topological --- Differentiable dynamical systems --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamique différentiable. --- Théorie ergodique. --- Dynamique topologique. --- Dynamique différentiable. --- Théorie ergodique.

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