Lectures:

In this page we'll post useful information about the lectures: source codes, data, references, etc...

• Introduction
• One-dimensional maps
• Two-dimensional maps
• Chaos
• Fractals
• Chaos in 2D
• Bottom of page

Matlab:

• A practical introduction to Matlab (HTML [PDF], PDF)
• Matlab Help

Maple:

• Maple Workshop notes

Lab:
GMCS-422 computer lab

Intro:

• Fractal: basin of attraction for an magnetic pendulum: [pptx intro]
  
  
  

• Fractal: the Mandelbrot set: self similarity (click on image)
  

• Java applet to navigate through the Mandelbrot set
• The butterfly effect: Lorenz attractor

One-dimensional maps:

• Desmos app for cobweb plotting: logistic map , (3x-x^2)/2 map


• Cobweb ploting: cobweb.m
  

• Bifurcation diagram of period 1,2,3 and 4 orbits (Maple): logistic_p1p2.mw logistic_p1p2.pdf
  

• Bifurcation diagram for the logistic map: logistic_bif.m.
  
  
  
• Sensitive dependence to ICs: sensitive.m
  

Two-dimensional maps:

• Poncaré and the 3-body problem: Flash demo, Wolfram Demo
  
• The Hénon map: henon.m
  
• Period-2 orbit of the Hénon map: henon_p2.m
  
• Source and sink behavior near fixed points: henon_local_dyn.m
  
• Linear maps: linear_map.m
  
• Stability of fixed points for the Hénon map: henon_stab_fp.m
  
• Stability of periodic orbits for the Hénon map: henon_stab_period.m
  
• Bifurcation diagram for the Hénon map: henon_bif.m
  
• Basin of attraction for period-2 orbits the Hénon map: henon_basin_p2.m
  
• Manifolds for the fixed points of the Hénon map:
  
• Manifolds for the period-2 orbits of the Hénon map:
  
• Manifolds of the trivial fixed point of the map arising from vibrations of Bose-Einstein condensates trapped in optical lattices:
  
  

Chaos:

• Conjugacy between logistic and tent maps: conjugacy.m
  
• Density of chaotic orbits in the logistic map: dense.m
  
• Basin of attraction for a generic sink: generic_sink.m
  

Fractals:

• The fern tree fractal: fern.m.
  
  
  
• Iterated Function Systems (IFS):
  Cantor Set: IFS_1D_2f.m, Sierpinsky triangle:IFS_2D_3f.m, Sierpinsky carpet: IFS_2D_4f.m.
  
  
  
• Self similarity of the Hénon fractal attractor: henon_selfsim.m.
  
  
  
• Riddled basins of attraction: riddled.m.
  
  
  
• Mandelbrot set: mandelbrot.m.
  
  
  
• Julia sets: julia.m, animations of Julia sets
  
  
  
• Box counting dimension: box_counting_dim.m
  
  
  
• Computing distance matrix: dist_matrix.m
  
  
• Correlation dimension: correlation_dim.m
  
  
  
• Fitting a polynomail to data: fit.m
  
  
  
• Histogram using matlab: henon_histogram.m
  
  
  

Chaos in 2D:

• The cat map.
  
  
• Matrix times circle equal ellipse: matrix_circle_ellipse.m.
  
  
  
• Gram-Schmidt orthonormalization: GS_rcg.m.
  
  
  
• Horseshoe for the Hénon map: henon_horseshoe.m.
  
  
  
• Trapping region for the Hénon map: henon_trapping.m.
  
  
  
• Probability density function: pdf.m, pdf_evolution.m.
  
  
  
• Lyapunov exponents for a discrete system using QR: lyapunov_QR_2D.m.
  
  
  
• Lyapunov exponents for a discrete system using J*transpose(J): lyapunov_JJt_2D.m.