## Syllabus

(The tentative schedule)

Week 1
Mon 16 Sept  1.1-1.3: Discrete maps, fixed points, cobwep plots, stability
Worksheet 1
Solutions
Weds 18 Sept  1.4-1.5: Periodic points, logistic maps, bifurcation diagram
Worksheet 2
Solutions
Thurs 19 Sept Learn how to use Matlab: download `intro53.m`
Fri 20 Sept
1.6-1.7:  "Periodic table" of logistic map 4x(1-x), sensitive dependence on initial conditions  Worksheet 3
Solutions
Week 2
Mon 23 Sept
1.8: Itineraries
Notes on change to theta  Sensitivity code for f(x) = 3x(mod 1)
Worksheet 4
Solutions
Weds 25 Sept
2.1-2.2: Poincare maps, Sinks, Sources and Saddles
`explormap2d.m`    `explorbasin2d.m`    `iterdisc2d.m`

Thurs 26 Sept
2.3-2.4: Linear maps and coordinate changes
Worksheet 5
Solutions
Fri 27 Sept
Visit by Tristan Perich

Week 3
Mon 30 Sept
2.5: Nonliner maps and the Jacobian
Weds 2 Oct
2.6: Stable/unstable manifolds  Worksheet 6
Solutions
Thurs 3 Oct

Fri 4 Oct   2.7: disc under linear map `iterdisc2d.m`
End of material covered by midterm 1
Worksheet 7
Solutions
Week 4
Mon 7 Oct
3.1-3.2: Lyapunov Exponents, Chaotic orbits, binary  Worksheet 8
Solutions
Tues 8 Oct  Midterm 1, 5:00-7:00 pm, Kemeny 201 Exam 1    Solutions
Old midterms:  2007 midterm 1  solutions  2009 midterm 1  solutions    2011 midterm 1  solutions
Weds 9 Oct
3.3: Conjugacy and the Logistic Map
Thurs 10 Oct

Fri 11 Oct
3.4: Transistion Graphs and Fixed points  Worksheet 9
Solutions
Week 5
Mon 14 Oct
4.1: Cantor Sets

Weds 16 Oct
4.2: Probabilistic constructions of fractals
Iterated function system  Chaos games
Worksheet 10
Solutions
Thurs 17 Oct
4.3: Fractals from deterministic systems
Fri 18 Oct
4.4: Fractal Basin Boundaries
Worksheet 11
Solutions
Week 6
Mon 21 Oct
4.5-4.6: Fractal dimension, The box-counting dimension
Mandelbrot movie
Worksheet 12
Solutions
Weds 23 Oct
4.7: Correlation dimension

Thurs 24 Oct

Fri 25 Oct
5.1-5.2: Lyapunov exponents, numerical computation of the exponent

Week 7
Mon 28 Oct
5.2 Numerical computation of the Lyapunov exponent

Tues 29 Oct  Project 1-2 page description due.
Weds 30 Oct
7.1-7.2: 1-D linear and nonlinear differential equations
Thurs 31 Oct

Fri 1 Nov
7.3-7.4: Nonlinear systems of ODEs, stability.
code: potential1d.m.
Math 23 worksheets on 1st order systems
Math23: Worksheet 20
Math23: Worksheet 21
Week 8
Mon 4 Nov
7.5 Motion in potential field  Worksheet 13
Solutions
Tues 5 Nov
Weds 6 Nov
7.6: Damping in potential field, damped pendulum. Lyapunov functions
End of material covered by midterm 2

Thurs 7 Nov
Midterm 2, 5:00-7:00 pm, Kemeny 201

Fri 8 Nov
8.1: Range of flow limit behaviors in R and R2: Poincare-Bendixson theorem
Week 9
Mon 11 Nov
8.2: Chaos in ODEs: Lorenz attractor.
Weds 13 Nov
9.6:Measuring Lyapunov exponent in flows lyapflow
(needs lorenz_time1map.m)

Thurs 14 Nov

Fri 15 Nov  Student presentations
Week 10
Mon 18 Nov  Student presentations
Weds 13 Nov

Thurs 14 Nov

Fri 22 Nov  Projects are due