LisMath Seminar 

10/10/2018, 17:00 — 18:00 — Room P9, Mathematics Building
Carllos Holanda, LisMath, Instituto Superior Técnico

Applications of ergodic theory to number theory

Ergodic theory can be described as the study of measurable maps and flows preserving a certain measure. Some emphasis is given to the study of the recurrence properties and stochastic properties of the dynamics. It turns out that there are many nontrivial applications of ergodic theory to number theory. As an illustration, we shall consider fractional parts of polynomials and continued fractions.

Bibliography:

[1] L. Barreira, Ergodic Theory, Hyperbolic Dynamics and Dimension Theory, Springer, 2012.

[2] H. Weyl, Ueber die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), 313-352.

See also

Lismath_Seminar_Carllos_Holanda.pdf