عنوان

Ergodic theory and dynamical systems in their interactions with arithmetics and combinatorics :

3319749080

9783319749082

3319749072

9783319749075

Ergodic theory and dynamical systems in their interactions with arithmetics and combinatorics :

[Book]

CIRM Jean-Morlet Chair, Fall 2016 /

Sébastien Ferenczi, Joanna Kułaga-Przymus, Mariusz Lemańczyk, editors.

Cham, Switzerland :

Springer,

2018.

1 online resource (xiv, 434 pages) :

illustrations (some color)

Lecture notes in mathematics,

2213

0075-8434 ;

Part I. Bases of Analytic Number Theory -- 1. Prime Numbers -- 2. Arithmetic Functions -- 3. Dirichlet Series -- 4. Euler Gamma Function -- 5. Riemann 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 Conjecture -- what new -- 12. Sarnak 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 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.

0

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.

Springer Nature

com.springer.onix.9783319749082

Ergodic theory and dynamical stystems in their interactions with arithmetics and combinatorics.

9783319749075

Ergodic theory.

Number theory.

Combinatorics & graph theory.

Ergodic theory.

Geometry.

Mathematics-- Combinatorics.

Mathematics-- Geometry-- General.

Mathematics-- Mathematical Analysis.

Mathematics-- Number Theory.

Nonlinear science.

Number theory.

Number theory.

MAT034000

PBWR

Ferenczi, Sébastien

Kułaga-Przymus, Joanna

Lemańczyk, Mariusz

20200823105353.0

pn

[Book]

Y