Topics for Final, Math 313-1, March 2003
The following topics have been covered in this course.
Problems relating to each topic from previous tests are given;
02T1#1 refers to problem 1 on Test 1 from 2002,
92T#1b refers to problem 1b from the (only) test in 1992, etc.
- Topics on Test 1
 
- Calculate periodic orbits and count periodic orbits:
Sections 2.1
- HW 2.1.2, 2.1.3, 2.1.4
- 03T1#1; 02T1#1,#2; 02F#1; 99T#1; 98T#2
- Graphical method of iteration: Section 2.2
- HW 2.2.1
- 03T1#2b ; 02T1#3b; 02F#2b; 99T#2b; 99F#1b; 98T#3b; 92T#1b; 92F#1b
- Stability: Sections 2.3,
- HW 2.3.1, 2.3.6, 2.3.8, 2.3.9
- 03T1#2a,#3; 02T1#3a; 02F#2a; 99T#2a; 99F#1a, #6a; 98T#1; 98F#2, #6;
98T#3a; 92T#1a; 92F#1a, #2
- Cascade of orbits: Section 2.5
- Schwarzian derivative: Section 2.4.
- HW 2.4.1, 2.4.2
- 03T1#4; 02T2#1a; 02F#4a
- Applications: Section 2.7.
- Conjugacy: Section 2.6. (not on either test)
- HW 2.6.1
- 02T2#3; 99T#3; 92F#4
 
- Topics on Test 2
 
- Periodic orbits from transition graphs, including
Sharkovkii Theorem: Sections 3.1
- HW 3.1.1, 3.1,2, 3.1.3
- 03T2#1; 02T2#2; 99F#5; 98F#3
- Topological Transitivity and symbolic dynamics:
Section 3.2
- HW 3.2.1, 3.2.3
- 02T1#4; 92F#3bc
- Sensitive dependence: Sections 3.3,
- HW 3.3.1, 3.3.5
- 03T2#2; 92F#3a
- Cantor sets : Section 3.4
- HW 3.4.1, 3.4.2
- 03T2#3; 02T2#4; 02F#3acd; 99F#4; 92T#3; 99F#4;
- Subshifts for piecewise expanding maps: Section 3.5.
- HW 3.5.1
- 03T2#4; 02F#5abcf;
- Applications: Section 3.6.
 
- Topics after Test 2
 
- Limit sets: Section 4.1
- Chaotic attractors: Section 4.2
- HW 4.2.1, 4.2.2, 4.2.3, 4.2.6
- 02F#5ei
- Lyapunov exponents
- HW 4.3.1
- 02T2#1bc; 02F#4bc, #5g; 99T#4a; 99F#6bc; 92F#5