About the Project

The idea to implement a joint project with the School of Mathematical Sciences at Tongji University arose naturally, as we have long-standing scientific connections with our Chinese partners and experience in successfully carrying out a number of similar projects. The staff of our laboratory has visited Jinhua University multiple times for scientific purposes and there are several jointly obtained scientific results. This project was conceived as an opportunity to expand the spectrum of scientific tasks, gain experience working in a new international team, and receive a boost for development while fostering collaboration between scientific schools with different traditions and approaches. Due to its applied nature, dynamic systems is a sufficiently popular area of mathematics. In particular, the Chinese team has significant experience working in both regular and chaotic dynamic systems.

Project Aims

The main scientific goal of the research is to obtain new knowledge about dynamic systems, including expanding the set of systems for which the question of the existence of an energy function is resolved, obtaining fundamental results related to the classification of hyperbolic dynamic systems and their attractors, as well as describing the relationship between the structure of the non-wandering set of a dynamic system and the topology of the manifold on which it is defined.

The main educational goal of the research is to involve students and graduate students in project-based scientific activities. At this stage, a significant part of the laboratory team consists of promising young mathematicians. For some of them, this project is their first experience working in an international team. In addition, the research conducted will contribute to the development of special courses on the theory of dynamic systems and the writing of methodological manuals describing the obtained scientific results and modern methods. The results of the research will be presented at a scientific seminar organised by the laboratory, and new tasks arising in the process of conducting the research will be proposed as dissertation topics. One of the applied aspects of the research is the possibility of modelling deterministic processes in the natural and social sciences.

Project page with linked publications (in Russian).