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, ...
• ...

Quick links

• 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)

Organization

We plan organize the sage.dynamics repository with 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 (?)

Subprojects

• Arithmetic and Complex Dynamics

• dynamics/FlatSurfaces

• LanguagesAndTilings

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