Ergodic Theory with a view towards Number Theory
We develop the beginnings of ergodic theory and dynamical
systems.
The selection of topics has been made with the applications
to number theory in mind.
We follow the book
Manfred Einsiedler, Thomas Ward.
Ergodic Theory with a view towards Number Theory.
GTM 259, Springer.
A focus will be on chapters 2 and 7, using additional material as required.
Doing problem sets is obligatory for credits. The course will be graded in an oral exam.
The course will be given as a reading course; the first period we meet on Thursdays at 13:30
in the office C4.151 of Ale Jan Homburg.
List of topics treated
per week
- Week 1, February 9
Motivation, Sections 1.1,1.2,1.3
Ergodicity, Recurrence and Mixing, Section 2.1
- Week 2, February 16
Ergodicity, Recurrence and Mixing, Sections 2.2, 2.3
Problem set 1.
Hand in solutions before the lecture on March 1, containing solutions to at least three out of five problems.
- Week 3, February 23
Ergodicity, Recurrence and Mixing, Section 2.4, 2.5
- Week 4, March 1
Ergodicity, Recurrence and Mixing, Section 2.6
- Week 5, March 8
Ergodicity, Recurrence and Mixing, Section 2.7, 2.8, 2.9
Problem set 2.
Hand in solutions before the lecture on March 22.
- Week 6, March 15
Invariant Measures for Continuous Maps, Section 4.1, (4.2 if you like,) 4.3
(without Theorem 4.14)
- Week 7, March 22
Invariant Measures for Continuous Maps, Section 4.4.1, 4.4.2
(I am away from office this week,
reachable by email)
(Note for homework: I have a mailbox both at UvA and at VU)