# Christian Henriksen

Associate Professor

Department of Applied Mathematics and Computer Science

Asmussens Allé

Building 303B Room 154

2800 Kgs. Lyngby

Danmark

Mathematics in Industry Dynamical systems Applied Mathematics

Research interests. I am interested in complex analytical dynamical systems and applications of mathematics within industry. When a systems evolves with time in a way that can be described mathematically, then one calls it a dynamical system. The motion of the planets in the solar system, and the balance of an savings account from term to term when interest is applied, are two examples of dynamical systems. In the first example, time varies continuously, whereas in the second time jumps from term to term. In the latter case, we say time is discrete. I am interested in dynamical systems where time is discrete, the state is given by one or more complex numbers, and the rule dictating the evolution of the system is a complex analytic function. It turns out, that complex analytical dynamical systems can behave in two different ways. In an orderly fashion where you can make long term predictions, and in a chaotic fashion where long terms predicitons are impossible. This dichotomy between order and chaos gives rise to complicated geometric figures known as fractals. The study of dynamical systems and fractals is an exciting field where algebra and geometry, as well as analysis and combinatorics meet. There are many applications of mathematics, you can even consider the natural sciences as applied mathematics, and not surprisingly mathematics also play an important role within industry. It fascinates me, how classical mathematics is useful in a tecnical context. Whether it is geometry, statistics, dynamical systems or something else entirely is not important to me; that it can be instrumental in finding solutions is what matters. European Study Groups with Industry, ESGI, is a good example where mathematics can contribute to industry, and industry can supply good problems to mathematics. In a study group, industry representatives pose problems to industry and then work together with a group of mathematicians intensively for a week on solving these problems. Afterwards reports are written describing the progress made. In my experience both industry representatives and mathematicians learn a lot from these sessions.