Syllabus


Lectures Brief Description Sections in Text
9/11 Introduction: Discrete and Continuous-time Dynamical Systems, fixed points
Here is a roughly annotated and extended version of the file we used during class (I removed the cobweb plot because that's your assignment).
Chapter 1.1, 1.2
9/13 Attracting fixed points (proof here!) and periodic points. Chapter 1.3, 1.4
9/15 Stability, doubling map, eventually periodic. Chapter 1.5
9/18 Bifurcations.
(Mathematica Bifurcations)
Bifurcation diagrams: full and chaotic region.
9/19 Proof Writing X-Hour, 12:15 pm
9/20 Chaos! Sensitivity to initial conditions, chaotic orbits.
9/22 Two dimensional linear maps. 2.2, 2.3, 2.4
9/25 Nonlinear maps and the Jacobian, Henon map. 2.5
9/27 Stable/unstable manifolds, Henon map.
Henon Map Animations.
2.6
9/29 Lyapunov exponents.
Logistic Lyapunov Animation.
3.1, 3.2
10/2 Itineraries, transition diagrams. 1.8, 3.3
10/4 Lyapunov exponents, flat-topped tent map.
Lyapunov and Cobweb for Logistic
Flat-topped Tent Map
10/5 Midterm Exam 7 pm, Kemeny 201.
10/6 Sarkovskii's Theorem. Three Implies Chaos.
10/9 Fractals arising from maps, Cantor set, fractal dimension.
10/11 Probabilistic construction of fractals, Koch Snowflake and others.
Mathematica Fractal File
Fractal Fern
10/13 Box-counting dimension.
Henon Strange Attractor
10/16 Julia and Mandelbrot sets; Basins of Infinity.
Mandelbrot and Julia Sets
10/18 Crash Course in Differential Equations (Review).
10/20 Limit Cycles: Poincare-Bendixson Theorem.
Stable Limit Cycles
10/23 Stable Manifolds, Limit Sets.
Monday Worksheet Solutions
10/25 Chaos in Higher Dimensions. Strange Attractors.
10/26 Midterm Exam 7-9pm
10/30 Attractors in Non-linear Systems
Lorenz Attractor and Delay Embeddings
11/1 Delay Embeddings and Shannon Entropy
11/3 Permutation Entropy, Generating Partitions, KL Divergence Methods
11/6 Recurrence Plots and Estimating Lyapunov Exponents
Sample Data
Example Recurrence Plots
11/8 Local Rules and Cellular Automata, Spread of Information on Graphs.
First Examples
11/10 More Cellular Automata
Langton's Ant, Game of Life.
11/13 Last day: talking about chaos.
11/17 Final Exam 8:00 am - 11:00 am


Katherine Moore
Last updated November 22, 2017