Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics

Beschreibung

This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Möbius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described.
This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Möbius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described.

Features a unique, exhaustive list of results and methods concerning the Sarnak and Chowla conjectures Includes a course in analytic number theory accessible to undergraduate students Offers a clear presentation of the interaction of modern dynamics with number theory and combinatorics

Autor*in

Sébastien Ferenczi

Themen in »Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics«

Analytic Number Theory Ergodic Theory Equidistribution Homogenous Dynamics Lagrange Spectrum Moebius Disjointness Multiplicative Functions Sarnak's Conjecture Chowla's Conjecture Translation Surfaces combinatorics

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