HONOURS M. A. AND HONOURS B. Sc. EXAMINATION
MATHEMATICS AND STATISTICS
Paper MT4508 Dynamical Systems
May 2004
Time allowed : Two hours
Attempt ALL questions
Consider the map f : R2 R2 dened in polar coordinates r 0, 0 < 2 by
1.
f (r, ) = (r 2 , sin ).
(
Example Solutions
Course
Lecturer
Academic Year
:
:
:
Dynamical Systems (MT4508)
T. Neukirch
2009/2010 (Semester 2)
Question 1
Solution :
(a)
We expect two equilibria (one at x = 0), because there are two intersections
between y = x and the graph of the m
MAY 2010 EXAMINATION DIET
SCHOOL OF MATHEMATICS & STATISTICS
MODULE CODE:
MT 4508
MODULE TITLE:
Dynamical Systems
EXAM DURATION:
2 hours
EXAM INSTRUCTIONS Attempt ALL questions.
The number in square brackets shows the
maximum marks obtainable for that que
Purpose
Course
Lecturer
Academic Year
:
:
:
:
Example Solutions of Exam Questions
Dynamical Systems (MT4508)
T. Neukirch
2003/2004 (Semester 2)
Question 1
Solution :
(i)
We have
r = r2
=
r = 0, 1 ,
and
= sin
=
sin = 0
=
= 0, .
for 0 < 2 . Since r = 0 i
Purpose
Course
Lecturer
Academic Year
:
:
:
:
Example Solutions of Exam Questions
Dynamical Systems (MT3808/4808)
T. Neukirch
2001/2002 (Semester 2)
Question 1
Solution :
(i)
Fixed points: We get
x = ax x3
x3 + (1 a)x = 0.
=
We conclude that
x=0
is a xed
Purpose
Course
Lecturer
Academic Year
:
:
:
:
Example Solutions of Exam Questions
Dynamical Systems (MT3808/4808)
T. Neukirch
1999/2000 (Semester 2)
Question 1
Solution :
(i)
Fixed points: For x 1/2 we get
x = ax
=
x = 0.
x = a ax
=
x=
For x > 1/2 we get
1
('1)
(ii)
(iii)
M zsog
U
HONOURS M. A. AND HONOURS B. So. EXAMINATION
MATHEMATICS AND STATISTICS
Paper MT3808 Dynamical Systems
May 2000
Time allowed : Two hours
Attempt not more than THREE questions
The tent map Ta(a;) (a. 6 IR) is dened by