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Dynamics in Sage = 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
  * [[https://lma.metelu.net/mailman/listinfo/sage-dynamics|sage-dynamics]]: lma.metelu.net mailing-list
  * [[http://groups.google.com/group/sage-dynamics | sage-dynamics]]: Google group (web forum + mailing list)
  * [[combinat|combinat wiki]]: the wiki page of the combinat community (see in particular the following [[combinat/Installation|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 ==

  * [[dynamics/ArithmeticAndComplex|Arithmetic and Complex Dynamics]]
  * [[dynamics/FlatSurfaces]]
  * [[LanguagesAndTilings]]

== Other programs ==

 * [[http://homepages.math.uic.edu/~culler/chaos/|Fractal, chaos and complex dynamics]] by M. Culler and H. Masur: educational purpose software
 * [[http://www.math.uiuc.edu/~nmd/computop/|computop.org]] references several interesting softwares, many of them written in python

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, ...
  • ...

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

Other programs

dynamics (last edited 2013-11-02 21:51:25 by vdelecroix)