Welcome to a full-year introductory course in Dynamical Systems, with emphasis on Ergodic Theory (measure-theoretic dynamics) and elementary Topological Dynamics. Depending on time and student-interest, we may cover some Symbolic Dynamics. The Second semester will continue with Entropy and then focus on Joinings (of measures and transformations), a topic of active research.

Our Teaching Page has useful information for students in all of my classes. It has my schedule, LOR guidelines, and Usually Useful Pamphlets. One of them is the Checklist The checklist

(pdf) which gives pointers on what I consider to be good mathematical writing. Further information is at our class-archive URL (I email this private URL directly to students).

Computer	Chalk	E-Probs	Blackboard	Time
Joe	Adam	Nick	Nick	James

The final project, Home-B (pdf)
Here is a stopping-time proof of the Birkhoff Ergodic thm (pdf), with slightly more detail than the handout from class.
Here is Home-A (pdf).

Fri, 23Oct: Today's Class-A (pdf) was so wildly popular that we decided to only have take-home exams in the future.

Mini-HW4 (pdf), due Wedn, 07Oct. This is an undergraduate combinatorics problem. My main reason for this tiny HW is the Addendum, which uses Birkhoff's thm to rule out a certain kind of semi-conjugacy.
HW3 (pdf), due Wedn, 30Sep2009. with defns of density of a set of integers, as well as set whose upper-density is five times its lower-density.
HW2 (pdf) and HW1 (pdf). Our HW0 (pdf) was discussed in class.

Our textbook for the first semester is Introduction to Dynamical Systems.

Authors:	Michael Brin & Garrett Stuck	ISBN-10:	0-521-80841-3
Year:	2002	Publisher:	Cambridge University Press

Here are links to this book at The Publisher's site and at Amazon.com.

Some Ergodic Resources of JLF King

Three Problems in search of a Measure (pdf). Companion article Billiards inside a cusp (pdf) (14 pages) proves that product measure is preserved under the billiard-flow, and solves a generalization of David Feldman's 1/x problem. There is a of the article.
Direct proof (no use of SMBreiman) that Rank-1 maps have zero-entropy (pdf).
The Boole Transformation (pdf)

A particular example of a topological dynamical system is an IFS, Iterated Function System, which is simply a list of linear maps. (Well … contractive affine maps, actually.) Here are some low-resolution IFS examples I created using a project from MIT designed to teach children how to program.

Spr2010: MTG6402 7907 Ergodic.Thy/Dyn.Sys.2 MWF5 LIT233

Ergodic Theory & Dynamical Sys. 2

Greetings. This is a continuation of my Ergodic Theory & Dynamical Systems 1; it should be accessible to anyone who has had a Measure theory course, and knows what the L^p-spaces are. Helpful, but not necessary, would be the first few chapters of an introductory text (E.g. Walters, Petersen, Brin&Stuck).

End-of-semester Individual project

The Project will be due, slid u n d e r room 402 Little Hall my office door (Little Hall 402, Northeast corner) , by 4PM on Friday, 23April2010.

The final project, Home-C must be carefully typed, but diagrams may be hand-drawn.

At all times have a paper copy you can hand-in; I do NOT accept electronic versions. Print out a copy each day, so that you always have the latest version to hand-in; this, in case your printer or computer fails. (You are too old for My dog ate my homework.)

Please follow the guidelines on the Checklist (pdf, 3pages) to earn full credit.

Ergodic Resources on the Web

Entropy on the World Wide Web has links. Also see An Entropy Primer (pdf) by Chris Hillman.
Prof. Thomas Ward's site: Ergodic Theory at UEA.
An introduction to joinings in ergodic theory by Thierry De La Rue.
The Mathematical Atlas: 60: Probability theory and stochastic processes
Factbites: Ergodic theory.

Conferences:

This list is always incomplete.

Ergodic Theory, Geometric Rigidity… (2000)

There are many Ergodic Theory conferences each year. I will provide links to several, once the semester begins.

Departments & people:

This list is in no particular order. Of necessity, at all times it is incomplete.

Karl Petersen
Stanley Eigen
Paul Shields
Marcus Pivato had an online book called Stochastic processes…. What I find now that this has a link to Ergodic Theory, Stochastic Processes, and Information Theory.
Anthony Quas's Home Page
Vitaly Bergelson
Search: Ergodic Theory

Some UF faculty and visitors working in Dynamical Systems

If you find an omission in this list, please email me.

Our textbook for the second semester is Ergodic Theory via Joinings.

Author:	Eli Glasner	ISBN-10:	0-8218-3372-3
		ISBN-13:	978-0-8218-3372-8
Year:	2003	Publisher:	American Mathematical Society

Here is Glasner's text at the AMS with an overview, Table of Contents. and a review by Mathematical Reviews. Also available is a short errata sheet (pdf). Currently, there is a $20 discount for AMS members.

The price of Glasner's text at Amazon.com currently (as of 21Oct2009) equals the AMS (undiscounted) price, so you might want to support the AMS and purchase there.