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Aut2009: MTG6401 5780 Ergodic.Thy/Dyn.Sys.1 MWF5 LIT203

Ergodic Theory & Dynamical Systems 1 Ergodic thy

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 ChecklistThe 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).

The various Math czars who help out:

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

Here is the syllabus for the first semester (txt).

Available is the webpage from when I taught this course in Fall 2000 and Spring 2001. There are four homework assignments on the page.

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
Photo of text cover

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

[Image: Coffee cup] Some Ergodic Resources of JLF King

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 Ergodic thy

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 Lp-spaces are. Helpful, but not necessary, would be the first few chapters of an introductory text (E.g. Walters, Petersen, Brin&Stuck).


A putnam problem which leads to a dynamical system.


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 Checklist (pdf, 3pages) to earn full credit.



[Image: Coffee cup] Ergodic Resources on the Web

Conferences:

This list is always incomplete. 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.

Faculty 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
Photo of text cover

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.




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____End: Ergodic Theory