Dynamics in Sage

This page is an organization wiki for the implementation in Sage of various algorithms related to dynamics.

Introduction

Different aspects of dynamical systems involve computers

simulation and experimentation
numerical algorithms seen as dynamical systems
prospection of combinatorial structures associated to dynamical systems (infinite words, ...)
intrinsically discrete dynamics: shifts, cellular automata, ...
...

These wiki pages are intended for the coordination of the different programmers in Sage.

dynamics/examples: examples that are produced with the code of sage-dynamics
sage-dynamics: lma.metelu.net mailing-list
sage-dynamics: Google group (web forum + mailing list)
combinat wiki: the wiki page of the combinat community (see in particular the following installation instructions for installing sage-combinat on your computer)

We plan to create a *dynamics* repository at the root of Sage subdivided according to the following hierarchy

arithmetic_dynamics (?)
cellular_automata (?)
complex_dynamics (?)
shifts (sage-combinat)
- tilings (WangTile)
- substitutive shift
  - self similar interval exchange map
- s-adic shift
  - Sturmian
  - interval exchange maps
surface_dynamics (sage-combinat)
- flat_surfaces
  - origamis
  - veech_surfaces
  - linear suspensions of iet
- train_tracks
- hyperbolic_dynamics
  - geodesic flow
  - Fuchsian groups
- hamiltonian flows
  - logarithmic suspensions of iet
picewise (sage-combinat)
- interval_exchange_transformations and linear_involutions
- affine_iet
- interval_translation
- 2D (?)

== Other programs ==

Fractal, chaos and complex dynamics by M. Culler and H. Masur: educational purpose software
computop.org references several interesting softwares, many of them written in python