The project in which Mohammad Sadek, a Faculty Member at the Faculty of Engineering and Natural Sciences (FENS), was found eligible for support under the TÜBİTAK 1001 Program.
Mohammad Sadek's project, which was found eligible for support under the 1001 Scientific and Technological Research Projects Support Program, is titled "Some Intersection Problems in Polynomial Dynamical Systems".
In natural events, there are many processes defined over a period of time. For example, the spread of a certain sample (culture), or even the landing of an aircraft. Researchers study such processes in discrete dynamical systems. A discrete dynamical system is a formula that can describe a given value, for example the size of a (culture) colony or the height of an aircraft at a given time. The idea of iteration is one of the fundamental ideas within discrete dynamical systems. If we know that the size of a colony increases at a constant rate every second, then we can define the size of the colony in a given second by looking at the previous second. In other words, the person repeats the formula as much as necessary, producing a series of values, often called the trajectory of the first value.
In our project, we are interested in arithmetic dynamical systems. These are discrete dynamical systems in which the formula is defined by a polynomial or rational map, and the values are integers or fractions of integers. The project aims to investigate the common values that occur in the finite trajectories of at least two such dynamical systems. In fact, in this project, we aim to be able to build dynamic systems with many common values.
Mohammad Sadek noted the following regarding the significance of the project: “Arithmetic dynamics is a young interdisciplinary field of research by nature.It aims at the possibility of enriching different branches of mathematics by conveying ideas, tools, and techniques.We believe that the project will attract the attention of many numerical theorists in Turkey to this field of research.”
Özlem Ejder from Boğaziçi University will support the three-year project led by Mohammad Sadek, a Faculty Member at FENS.