This article comes from the journal Science et Avenir – Les Indispensables n° 206, dated July/September 2021.
Olga Paris-Romaskevich is a mathematician and researcher at CNRS. he answered the questions of science and the future.
Science et Avenir: Can you tell us what dynamic systems are in your area?
Olga Paris-Romaskevich: Dynamics is motion, as opposed to statics. The study of a dynamical system is equivalent to defining the instantaneous change of an evolutionary event. For example, we can associate the bloom of a flower with a sequence of pictures taken every second: from one photograph to the next, we observe the movement of the flower. My goal as a dynamicist is to understand what will happen in the very long run if we continue with these photo suits. In this example, the flower eventually withers and stops moving! But for dynamical systems, the interesting moment is “at infinity”. The goal is to understand infinite motion in its totality, and without examining all developments, all trajectories.
How long has this domain existed?
It is much smaller than number theory, which appeared millennia ago with mathematical thought. Dynamic systems developed in the mid-19th century around questions related to the understanding of planetary motion. Since then, the area has exploded, and this question is only one of many. For my part, I am interested in paving in the subfield of billiards.
Trajectory, billiards, paving … Do these simple and concrete words have the same meaning here as in everyday life?
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