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Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics: CIRM Jean-Morlet Chair, Fall 2016 de Sébastien Ferenczi

Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics: CIRM Jean-Morlet Chair, Fall 2016: Lecture Notes in Mathematics, cartea 2213

Editat de Sébastien Ferenczi, Joanna Kułaga-Przymus, Mariusz Lemańczyk
en Limba Engleză Paperback – 16 iun 2018
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.
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Specificații

ISBN-13: 9783319749075
ISBN-10: 3319749072
Pagini: 390
Ilustrații: IV, 434 p. 231 illus., 8 illus. in color.
Dimensiuni: 155 x 235 x 27 mm
Greutate: 0.63 kg
Ediția:1st ed. 2018
Editura: Springer International Publishing
Colecția Springer
Seria Lecture Notes in Mathematics

Locul publicării:Cham, Switzerland

Cuprins

Part I. Bases of Analytic Number Theory.- 1. Prime Numbers.- 2. Arithmetic Functions.- 3. Dirichlet Series.- 4. Euler’s Gamma Function.- 5. Riemann’s Zeta Function.- 6. The Large Sieve.- 7. The Theorem of Vinogradov.- 8. The van der Corput Method.- Part II. Interactions Between Arithmetics and Dynamics.- 9. A Brief Guide to Reversing and Extended Symmetries of Dynamical Systems.- 10. Kloosterman Sums, Disjointness, and Equidistribution.- 11. Sarnak’s Conjecture – what’s new.- 12. Sarnak’s Conjecture Implies the Chowla Conjecture Along a Subsequence.- 13. On the Logarithmic Probability that a Random Integral Ideal is A-free.- 14. The Lagrange and Markov Spectra from the Dynamical Point of View.- 15. On the missing Log Factor.- 16. Chowla’s Conjecture: From the Liouville Function to the Moebius Function.- Part III. Selected Topics in Dynamics.- 17. Weak Mixing for Infinite Measure Invertible Transformations.- 18. More on Tame Dynamical Systems.- 19. A Piecewise Rotation of the Circle, IPR Maps and Their Connection with Translation Surfaces.

Textul de pe ultima copertă

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.

Caracteristici

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