Spring 2018 110.421 Dynamical Systems Syllabus

The details of this material may be updated and reformed as the semester progresses.

Week	Sections in Text PDF	Homework	Due	Selected Solutions
January 30 – February 1 01/30, 02/01	Course Orientation Chapter 1; What is a Dynamical System?	Problem Set 1	February 8	Solutions
February 6 – 8 02/06, 02,08	2.1 Preliminaries 2.2 The Contraction Principle	Problem Set 2	February 15	Solutions
February 13 – 15 02/13, 02/15	2.3 Interval Maps	Problem Set 3	February 22	Solutions
February 20 – 22 02/20, 02/22	2.3 Interval Maps	Problem Set 4	March 1	Solutions
February 27 – March 1 02/27, 03/01 http://bit.ly/2CSoJxv	2.5 Quadratic Maps 3 The Objects of Dynamics	Problem Set 5	March 8	Solutions
March 6 – 8 03/06, 03/08 http://bit.ly/2I81P9g http://bit.ly/2Ic6pmY	4 Linear Maps of the Plane	Problem Set 6	March 15
March 13 – 15 03/13, 03/15 http://bit.ly/2IpNRzS	5.1 Rotations of the circle 5.2 Weyl's Equidistribution Thm 5.3 Toral Flows 5.3.2 App: A polygonal billiard	Problem Set 7	March 29
March 20 – 22	Spring Break
March 27 – 29 03/27, 03/29 http://bit.ly/2GhNmGy http://bit.ly/2IaLoIv	5.4 Toral translations 5.5 Circle homeomorphisms 6.1 Incompressibility 6.2 Newtonian Systems	Problem Set 8	April 5
April 3 – 5 04/03, 04/05 http://bit.ly/2GylamQ	6.3 Poincare Recurrence 6.4 Billiards	Problem Set 9	April 12
April 10 – 12 04/10, 04/12	7.1 Counting Periodic Orbits 7.3 Chaos and Mixing	Problem Set 10	April 19
April 17 – 19 04/17,04/19	7.4 Sensitive dependence on initial cond. 7.5 Quadratic Maps	Problem Set 11	April 26
April 24 – 26 04/24,04/26	7.6 Complex dynamics 8.1 Topological Conjugacy 8.2.1 Lyapunov Expoenents	Problem Set 12	May 3
May 1 – 3 05/01,05/03	8.2.2 Capacity 8.2.3 Box Dimension 8.2.4 Topological Entropy	No homework

	Final Exam Slot	Thursday, May 17, 9am - noon.

Prof. Richard Brown		TTh 3:00pm - 4:15pm
brown “at” math.jhu.edu		Room: Krieger 309
403 Krieger Hall
410-516-8179
Office Hours:	M	2:00-3:00 pm	by appt. other times
	Th	1:00-2:00 pm

		The Text: R. Brown, A Modern Introduction to Dynamical Systems, 0^th edition, Oxford University Press (July 2018). PDF-version

	Course Material:	The material for this course is scattered throughout this text. We cannot possibly cover everything, but we will tour through most all of the topics.

	Grading Policy:	There will be homework sets, possibly a final exam, and maybe a project. The schedule of homework and the exams will be given below in time.

	Homework:	Homework based on the current week’s lectures will be posted here on the course web site sometime on Thursday after lecture. These assignments will be due the following Thursday in lecture. Mathematics is best learned in an environment where active discussion is a fundamental part of the learning process. You are strongly encouraged to work together in the understanding phase of the homework preparation process. You are required, however, to work alone when writing up homework solutions for submission. Homework is the essential educational part of this course. You will be graded not only on your ability to work through problems completely and concisely, but also on the presentation of your solutions and the arguments you make. It is the process with which you develop your argument that must be clearly and comprehensively represented in your proofs and calculations. If the audience (the reader of your submissions) must read between the lines to understand your arguments, then your work is not complete. This is a proof-based course. This means that many, if not most, of your homework problems will be to establish facts through argument rather than calculation. This means that you will be working with ideas more than numbers in many cases. I do understand that you may not be proficient at or have any experience in proof-writing. However, in time, you will adapt and learn.

	Course Policy:	You are responsible for lecture notes, any course material handed out, and attendance in class. There are no actual attendance requirements. However, I will easily get to know you and your rate of presence over time. And even though I will be using the book, the lectures will be serious embellishment of the material. *Good advice is the following: Treat the lectures as if you have already read the material and attempted some homework problems.* In this manner, you can focus mainly on parts of the lectures not found in the text or that covering areas of your reading you found difficult to understand. My teaching style is that of interactive discussion and I will rely on your input in developing the material. Active participation in the classroom is a great way to generate the discussion necessary to fully grasp the material.

	Help Room:	213 Kreiger Hall. The hours are 9am – 9pm on Monday through Thursday, and 9am – 5pm on Friday. This free service is a very valuable way to get one-on-one help on the current material of a class from other students outside the course. It is staffed by graduate students and advanced undergraduates. Outside of me and the Grader for the course, definitely take your questions to the Help Room. This course is simply an analysis course directed toward particular maps and differential equations. Most graduate students should be able to "see" through the many problems stated in this course. And your attempts to help guide them will be of huge benefit to you also.

	Ethics Statement:	The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Cheating is wrong. Cheating hurts our community by undermining academic integrity, creating mistrust, and fostering unfair competition. The university will punish cheaters with failure on an assignment, failure in a course, permanent transcript notation, suspension, and/or expulsion. Offenses may be reported to medical, law, or other professional or graduate schools when a cheater applies. Violations can include cheating on exams, plagiarism, reuse of assignments without permission, improper use of the Internet and electronic devices unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition. Ignorance of these rules is not an excuse. In this course, as in many math courses, working in groups to study particular problems and discuss theory is strongly encouraged. Your ability to talk mathematics is of particular importance to your general understanding of mathematics. You should collaborate with other students in this course on the general construction of homework assignment problems. However, you must write up the solutions to these homework problems individually and separately. If there is any question as to what this statement means, please see the professor or the grader. For more information, see the guide on "Academic Ethics for Undergraduates" and the Ethics Board web site (http://ethics.jhu.edu).