An Introduction to Holomorphic Dynamics
Fall 2019, MoWe 5:00-6:15 PM
Lippitt Hall 201

Instructor:    Araceli Bonifant  
Office: Lippitt Hall 202G
Phone: 874-4394

Office Hours:

Textbook: There is not required textbook. We will be using the notes of Professor Lasse Rempe-Gillen, who taught a similar class at the Department of Mathematical Science in Liverpool University. (I will provide copies of the Notes when the semester starts.)

Here are some further reading materials:

R. Devaney: An Introduction to Chaotic Dynamical Systems, 2nd Edition

J. Milnor: Dynamics in One Complex Variable, 3rd Edition (More advanced)

About the course: In this course we will explore the field of Complex Dynamics at an introductory level while reviewing, reinforcing, and extending the ideas learned in a typical first course on complex analysis. Julia sets and the famous Mandelbrot set will be introduced and interesting properties of their boundaries will be described. Towards the end of the course we will read a paper describing that the exponential map is chaotic.

The course will run as a seminar course. In the first class students will choose the first topic to present in class. Each student will have 60 minutes to present the material assigned to him/her +10 minutes or so for questions during the presentation. Each student will have to present twice during the semester (see course syllabus for details). Homework will be assigned regularly during the semester. The objective of the homework is to make sure that all students study the material in the book not just the part that they have to present.

Clicking here: Course Schedule you will get a detailed syllabus of the course. The syllabus may change a little, according to the needs of the class.

Grading: The grading will be based primarily on class participation (20%), the quality of the student's in-class presentations (50%), homework sets (30%). Not attending regularly will have a negative effect on the grade. Regular attendance is therefore required.

Reading: Zalcman's paper to complement the presentation of.

The exponential map is chaotic: An invitation to transcendental dynamics to complement the presentation of.

Homework: Homework problems will be posted here.

Accomodations. If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact the Disability Services for Students Office at 330 Memorial Union 401-874-2098. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.

Academic Integrity Statement. Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. Cheating is defined in the University Manual 8.27.10 as the claiming of credit for work not done independently without giving credit for aid received, or any unauthorized communication during examinations (of course, this includes the ``Internet''). Students are expected to be honest in all academic work. The resolution of any charge of cheating or plagiarism will follow the guidelines set forth in the University Manual 8.27.10-8.27.20.

Critical Incident Management Statement. The University of Rhode Island expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.