# Dynamical systems, measures and fractals via domain theory

## Abbas Edalat

(Imperial College)

Domain theory investigates properties of "continuous posets". It was introduced by Dana Scott in 1970 as a mathematical theory of computation in the semantics of programming languages, and since then, it has developed extensively in various areas of semantics. In recent years, a new direction for applications of domain theory has emerged as it was uncovered that there are indeed natural domain-theoretic computational structures in dynamical systems, measure theory and fractals. In particular, a computational framework for measure theory was established, which then led to a generalisation of the Riemann theory of integration with diverse applications.

We will give a survey of this work and describe a number of results and algorithms in the periodic doubling route to chaos and in the theory of iterated function systems, with applications in the one-dimensional random field Ising model, forgetful neural nets and fractal image compression. We also explain the basics of a programming language with a real number data type for exact real number computation which includes computing integrals.

**Tuesday 5th March 1996, 14:30**

Seminar Room 322

Department of Computer Science