The Importance of Admissible Maps Between Sequential Dynamical Systems

Tuesday, November 4, 2003 - 4:25pm - 5:00pm
Keller 3-180
Bodo Pareigis (Ludwig-Maximilians-Universität München)
Sequential dynamical systems have been used to simulate many different processes. It is desirable to study their mathematical properties. Much progress has come from studying their abstract mathematical structure.

I want to show the advantages to be gained by studying also admissible maps between them.

  • It is known that the full structure of a specific sequential dynamical system is known if one knows the set of all admissible maps originating in this object.

  • Admissible maps are the correct definition of a simulation of one sequential dynamical system by another such system.

  • Admissible maps can help to study the decomposition of a large sequential dynamical systems into small standard sequential dynamical systems.

  • They can help to find best simulations of other systems by sequential dynamical systems.

The best presently known definition of an admissible map will be given. The properties mentioned above will be discussed.