I plan to provide an introduction to the theory of dynamical systems as a rigorous discipline with many connections to the various areas of mathematics. The course will include several examples, which motivate theoretical concepts and methods.

See the daily diary for lecture notes and problem sets.

Topics

Topics will include topological dynamics, symbolic dynamics, ergodic theory, entropy, hyperbolic dynamics, one-dimensional dynamics, flows and differential equations.

Schedule of lectures

Monday 8:30-9:20 in 401 Stirling Hall.

Tuesday 10:30-11:20 in 401 Stirling Hall.

Thursday 9:30-10:20 in 401 Stirling Hall.

*** There will be no in-person lectures during Weeks 10-12 ***

*** Lectures will be delivered as a series of short videos, posted on our Class Diary page ***

Instructor

Francesco Cellarosi (fc19@queensu.ca).

Office hour: Monday at 2:30 in Jeffery 506 (or the 5th floor conference room).

*** There will be no in-person office hour during Weeks 10-12 ***

*** Every weekend, I will send out a link for an online meeting via Zoom on Monday at 2:30pm. Individual Skype / Zoom meetings at different times can also be arranged by email. ***

Audience

This course is aimed at 3rd and 4th year MATH majors, and at Masters/PhD students. Students in related disciplines (Statistics, Physics, Engineering, etc.) are also welcome.

Prerequisites

The only strict prerequisites for this course are:

• MATH/MTHE 281,
• MATH 231.

Although the MATH 328 is formally listed as a prerequisite, it is not strictly necessary. Students who have not taken MATH 328 and would like to enrol in MATH 427 should contact the Undergraduate Chair (mathstat.ugchair@queensu.ca) to obtain permission.

Textbook / Notes

While preparing this course, I have consulted several textbooks at various levels. The course will be based on a combination of materials from many different sources, and I will share my notes with the students. Notes will be posted in our Class Diary.

I highly recommend the book "A First Course in Dynamics, with a panorama of recent developments" by Boris Hasselblatt and Anatole Katok, 2003, Cambridge University Press, ISBN-10: 0521587506, ISBN-13: 978-0521587501. Errata are available here.

Grading scheme

*** Updated grading scheme ***

*** Homework: 50% ***

*** Project: 50% ***

*** The final exam has been cancelled ***

There will be 7 homework assignments during the semester. Graduate students (taking this course as MATH 827) will be required to submit additional problem set solutions. Homework will be assigned at the end of each week, see the Class Diary for details.

Further details about the projects may be found below.

Projects

*** Updated project deadlines and assessments ***

*** Oral presentations have been cancelled ***

• Each student is expected to learn a different theorem or topic, and write an expository paper on it. A list of topics is provided on the projects webpage.
• An outline and a rough draft will be due during the semester.
  • The outline will be graded by the instructor according to this checklist.
  • The rough draft of the paper will be graded by two other students according to this checklist. Each student will provide feedback and comments to the drafts of two other students (assigned by the instructor). The feedback will be graded by the instructor according to this checklist.
• After feedbacks are received, each student will write a final version of the paper. The written document must introduce, correctly state, and prove the theorem or topic. It should also include at least one interesting example illustrating the results. The document should be as self-contained as possible. The document must be typed, be at most eight pages in length (with 1 inch margins and 12 point font) and be available in PDF format.
• The final paper will be graded by the instructor, and receive the feedback of two other students (assigned by the instructor), according to this checklist. The feedback will be graded by the instructor according to this checklist.

Assessments and Deadlines:

*** Deadlines and percentages have changed ***

*** All project-related assignments should be submitted by email ***

• Outline (due Thursday, 27/02): 10% (checklist)
• Rough Draft (due Monday, 23/03): 15% (checklist)
• Feedback on other's draft (due on Tuesday, 31/03): 15% (checklist)
• Final Paper (due Wednesday, 15/04): 45% (checklist)
• Feedback on others' papers (due Sunday, 26/04): 15% (checklist)

Help, Accessibility, Inclusivity

If you are struggling or are feeling overwhelmed, do not hesitate to seek help and contact your instructor or Counselling Services. Also consult the Health Resources available to you. More information is available here.

Students with disabilities who will be taking this course and may need disability-related accommodations, are encouraged to contact Queen’s Student Accessibility Services (QSAS) to register for support services, and to make an appointment to see the instructor as soon as possible. Please review the Rights and Responsibilities for students with disabilities.

If you are a current Queen’s student with Aboriginal ancestry, you can self-identify any time through your SOLUS account, following the instructions provided here.

If you have a preferred name or pronoun that you would like your instructor to use when addressing you, please let me know. See the Inclusive Language Guidelines and the Human Right’s Office for further information. If you want, you can officially update your preferred name here. To educate yourself about pronouns, you are encouraged to read this publication by Queen's professor Airton Lee.