## 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
• HW 2.5.1
• Schwarzian derivative: Section 2.4.
• HW 2.4.1, 2.4.2
• 03T1#4; 02T2#1a; 02F#4a
• Applications: Section 2.7.
• HW 2.7.1

• 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
• HW 4.1.1
• 02F#5h
• 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