Instructor: Sylvain Bonnot
email: [email protected]
Office Hours: Tuesday 2 pm - 3 pm, Thursday 2 pm - 3 pm and by appointment.
Tutor: To be announced
Lectures: Tuesdays 3pm to 4pm in NE 144 and Thursdays 4pm to
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MAT 332 Assignment 3
1 Topological transitivity
1. Problem 10.2.1 (only part c).
2. Problem 10.2.2.
3. Problem 10.2.3.
2 Sequences of symbols
1. Problem 10.3.1
2. Problem 10.3.3 (only part a)
3 Sensitive dependence on initial conditions
1. Problem 10.4.1
MAT 332 Assignment 5
1. Problem 5.3.2 in textbook (only questions a,b and d)
2. Linearize the following linear systems at (0, 0) to show that it is an unstable fixed
point. Then produce a Maple plot showing that the system has a unique stable limit
MAT 332 Assignment 2
For each of the following functions, at the given parameter values, determine the bifurcations occuring if any (saddle-node or period doubling bifurcation)
1. F (x) = x + x2 + , at = 0
2. F (x) = x + x2 + at = 1
3. G (x
MAT 332 Assignment 4
1. Consider the non-linear system
x0 = y + ax(x2 + y 2 )
y 0 = x + ay(x2 + y 2 )
depending on the parameter a.
a) Linearize the system at the origin and verify that (0, 0) is a centre for the linearized
b) Use a Maple plot f
MAT 332 Assignment 1
1 Introductory material
1. What is the set of all real numbers x0 such that the sequence (xn0 )n1 is bounded
(justify your answer!).
2. Find all the points that are periodic with period 5 under the doubling map D.
3. What are the poss
Some Worked Out examples of nonlinear
1. Going back to our example of truly nonlinear system
Phase portrait studies of nonlinear systems.
Warning, the protected names norm and trace have been redefined and
Warning, the name adjoint has been redefined
Warning, the name changecoords has been red
Maple: Solving Ordinary Differential
A differential equation is an equation that involves derivatives of one or more unknown functions. Solving the differential equation means finding a function (or every such function) that
satisfies the differ