## Topics for Final, Math 313-1, December 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 9.1
• 03W-T1#1; 02T1#1,#2; 02F#1; 99T#1; 98T#2
• Graphical method of iteration & stability: Sections 9.2 & 9.3
• 03F-T1#1, 2a; 03W-T1#2, 3; 02T1#3; 02F#2; 99T#2; 99F#1, 6a; 98T#1, 3; 98F#2, #6; 92T#1; 92F#1, 2
• Bifurcation of periodic points: Sections 9.4,
• 03F-T1#4
• Schwarzian derivative: Section 9.5.
• 03F-T1#3; 03W-T1#4; 02T2#1a; 02F#4a
• Conjugacy: Sections 9.6,
• 03F-T1#2b; 02T2#3; 99T#3; 92F#4

• Topics on Test 2

• Periodic orbits from transition graphs, including Sharkovkii Theorem: Sections 10.1
• 03F-T2#1; 03W-T2#1; 02T2#2; 99F#5; 98F#3
• Topological Transitivity and symbolic dynamics: Sections 10.2 and 10.3
• 02T1#4; 92F#3bc
• Sensitive dependence: Sections 10.4,
• 03F-T2#3; 03W-T2#2; 92F#3a
• Cantor sets : Section 10.5
• 03F-T2#1; 03W-T2#3; 02T2#4; 02F#3acd; 99F#4; 92T#3; 99F#4;
• Subshifts for piecewise expanding maps: Section 10.6.
• 03F-T2#4; 03W-T2#4; 02F#5abcf;
• Applications: Section 10.6.

• Topics after Test 2

• Limit sets: Section 11.1
• 02F#5h
• Chaotic attractors: Section 11.2
• 02F#5ei
• Lyapunov exponents: Section 11.3
• 02T2#1bc; 02F#4bc, #5g; 99T#4a; 99F#6bc; 92F#5