MATH 326 Midterm: MATH326 Fall 2000 Exam
31 Jan 2019
School
Department
Course
Professor
Student Name:
Student Id#:
McGILL UNIVERSITY
FACULTY OF SCIENCE
FINAL EXAMINATION
MATH 326/376
Non Linear Dynamics and Chaos and Honors Nonlinear Dynamics and Chaos
Examiner: Professor A. Humphries Date: Thursday December 18, 2008
Associate Examiner: Professor D. Jakobson Time: 2:00 p.m - 5.00 p.m
INSTRUCTIONS
1. Students in MATH 326 answer any 6 questions.
2. Students in MATH 376 answer questions 3 through 8.
3. Please answer all questions in the exam booklets provided, starting each question on
a new page.
4. All questions carry equal weight.
5. This is a closed book exam. Notes and textbooks are not permitted.
6. Translation dictionaries (English-French) are permitted.
7. Calculators, including graphical calculators are permitted.
8. This exam comprises of the cover page and 3 pages of 8 questions.
Document Summary
Non linear dynamics and chaos and honors nonlinear dynamics and chaos. Notes and textbooks are not permitted: translation dictionaries (english-french) are permitted, calculators, including graphical calculators are permitted, this exam comprises of the cover page and 3 pages of 8 questions. In this case label the stable and unstable manifolds of the xed point, and the homoclinic orbit. (b) consider the dynamical system. U = au, u r2, where a is a 2 2 matrix. Give examples of a where the xed point at the origin is a: saddle, (linear) centre, unstable node, stable focus (stable spiral), stable star. You do not need to justify your answer: (do not do this question if you are a math376 student) consider the system. 4 x4. (a) consider the two-dimensional hamiltonian system. Sketch a phase portrait, and label the stable and unstable manifolds of any saddle points. (b) consider the general two-dimensional gradient system.
