Welcome to
F2009: MTG6401 5780 Ergodic.Thy/Dyn.Sys.1 MWF5 LIT203
Prof. Jonathan King squash@math.ufl.edu
Dept. of Mathematics http://www.math.ufl.edu/~squash/teaching.html
Office: 402 Little Hall (Top floor, NE corner) 392-0281 x270
[If I am not in the office then it is best to EMAIL me; I rarely pick-up
phone messages. If urgent, please telephone the secretaries at
392-0281.x221 and they can contact me at home.
Office hours: http://www.math.ufl.edu/~squash/info.jksched.html
My OHs will vary during the semester, so please check the webpage.
Currently, OHs are: Mond.: 7th. Wedn.: 8th & 9th periods.
Course page: http://www.math.ufl.edu/~squash/course.ergd.2009t.2010g.html
Archive: https://lists.ufl.edu/cgi-bin/wa?A0=FALL-5780-L
>> Please keep our archive private to our class. <<
To post to our class (and me), email to
FALL-5780-L@lists.ufl.edu (POST Erg)
Text: "Introduction to Dynamical Systems", 2002, by M. Brin & G. Stuck.
Cambridge University Press. (ISBN-13: 9780521808415 | ISBN-10: 0521808413)
SYLLABUS for the first semester: Chapters 1-4; overview of Topo. Dyn.,
Symbolic Dyn., Ergodic theory, as well as Entropy theory (topological
and measure-theoretic). We will do a detailed proof of the Variational
principle that topo-entropy is the supremum of m.t-entropies.
SYLLABUS for the 2nd semester will be partly determined by student interests,
with the intent of leading towards research problems.
EXAMS: In addition to sporadic quizzes, There will be 3 take-home team exams
(typed), with an in-class individual component. There will be NO final exam;
rather, a (typed) final project, due Friday, 11Dec2009 (LDClass+2).
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HOMEWORK: For b a real number, let R_b denote rotation by b on the
unit-circle. For each positive integer ("posint") K, show that R_{Kb} is a
factor of R_b. (I.e, there is a [continuous] "semi-conjugacy" from R_b onto
R_{Kb}.) Is R_{Kb} also a measure-theoretic factor?
For reals 0 =< b,c =< 1/2, prove: If R_b and R_c are topologically
isomorphic, then b=c. The same holds for m.t-isomorphism, but is harder to prove.
Please print-out and bring to class "Three Problems in search of a Measure",
which we will start perusing next week.
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CLASS-PHOTO DAY: Monday, 31Aug2009. Look sharp! Please
bring name-card with (optional but useful) your telephone number.
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