Dynamics at Cornell

Dynamics projects

Adaptive Stepsize
Visualization of limit sets of Kleinian Groups
Hénon map
- Complex parameter space pictures
  - From several programs
  - From SaddleDrop
- Real parameter space pictures
- Monodromies
- Dynamical space pictures
  - Unstable Manifold Slices
  - Siegel Balls
Newton's Method
- intersection of two quadratic curves in C²
  - Generic case
  - Degenerate case
- cubics: Mandelbrain parameter space pictures
- newtonAtInfinity
Rational maps
- Polynomial Matings by the Medusa Algorithm
Real 2D systems of ODE's or maps

Programs for download

Link	Summary
FractalAsm	(Mac) Explore any 2D dynamical system. Write your own definition. Color up to 8 attractors. Movies.
SaddleDrop	(Mac) Parameter space pictures for the Hénon map, by following critical points
Tangencies	(Mac) View Henon stable and unstable manifolds in R2, G+/G- tangency locus in R2, and NTL invariant.
AltiVec J-sets	(Mac) Julia sets in 16-bit color at 800x600, 60fps, on a 400MHz G4; achieves 3.2GFlops rate.
Medusa	(Unix) Computes normal form and postscript picture of mating of two quadratic polynomials.
Planar Maps and DE's	(Mac) Explore 2D systems of ODE's or iterated maps (draw stable/unstable manifolds, find periodic points, etc.).

Source Code is for download.

Papers for download

Ph.D. Dissertations:
- Suzanne Lynch Hruska, On the numerical construction of hyperbolic structures for complex dynamical systems, August 2002.
- David Brown, Using Spider Theory to explore parameter spaces, August 2001. [PDF, 2.6 MB]
- Ricardo Oliva, On the combinatorics of external rays in the dynamics of the complex Henon map, 1998. [PDF, 1.8 MB]

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