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Ergodic theory, spring 2015

Lecturer

Mikko Stenlund

Scope

5 sp.

Type

Advanced studies

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Prerequisites   

The student should know the basics of measure theory, Lebesgue integration and elementary topology, and be comfortable with the notions of Banach/Hilbert spaces (in particular L^p spaces) and bounded linear operators on them. We will use several theorems (Hahn–Banach, Riesz representation, Radon–Nikodym, ...) from real and functional analysis, which will be recalled during the lectures; the courageous student could take the course without prior knowledge of these results, but understanding the precise statements is essential, for which the mentioned prerequisites are key.

Lectures

Period IV (9.3.–3.5. excluding Easter break 2.4.–8.4.) as follows:

Tuesdays and Fridays 14:15–16:00 in room CK111 (Exactum). Exception: Tuesday 21.4. in B119.

Bibliography

[Lecture notes] – Version: March 30; consider printing only what you really need on paper as the notes are evolving.

Registration

Registration should be done through [WebOodi]. (Once logged in, look up the course by entering Ergodic theory in the search field.)

Office hours

Please schedule a meeting by email on all matters, including assistance with homework.

Exercises

Mondays 14:15–16:00 in room CK108 (Exactum). First session March 23.

  • Set #1: (1) 2.6 & 2.7; (2) 2.11; (3) 2.16; (4) 2.22; (5) 2.23; (6) 2.26 . Note: numbers refer to the March 18 version of the notes.
  • Set #2: (1) 2.32; (2) 2.35; (3) 2.42; (4) 2.43; (5) 2.47; (6) 2.51.
  • Set #3: (1) 3.8; (2) 3.11; (3) 3.13; (4) 3.17; (5) 3.22; (6) 3.24.
  • Set #4: (1) 3.29 & 3.31; (2) 3.32; (3) 4.6; (4) 4.8; (5) 4.12; (6) 4.13. (A tiny bit of Fourier analysis required in (3) & (4).)
  • Set #5: (1) 3.14; (2) 4.22; (3) 4.24; (4) 4.25; (5) 4.30; (6) 4.31. ((5) & (6) require studying the proof of Theorem 4.29.)
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