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Dynamics of Homeomorphisms, Noninvertible Maps and Flows with Respect to Minimality


The project is in the area of Topological Dynamics, one of the main branches of the Theory of Dynamical Systems. We study minimality in discrete-time dynamical systems given by noninvertible continuous maps or homeomorphisms, as well as in continuous-time dynamical systems given by continuous flows.

Our attention will be focused on, but not reduced to, the following problems:
1. Existence of minimal maps and/or homeomorphisms on manifolds and more general spaces;
2. Classification of minimal sets on manifolds and more general spaces;
3. Denjoy minimal sets;
4. Cantor minimal systems and their embeddings into manifolds;
5. Existence of minimal flows - the Gottschalk Conjecture and related problems.

In the research we will use various techniques from different areas of mathematics - besides the theory of dynamical systems, mostly from algebraic topology, general topology, mathematical analysis, etc. We want to reach the results by bringing together the expertise of the applicant with that of the host institute.

We can summarize the relevance of the project to the objectives of EIF in the following points:
1. reinforcing professional maturity of the applicant by adding scientific competencies;
2. diversifying the applicant's expertise;
3. involving research teams from less-favoured regions;
4. producing and supporting long-term synergies;
5. building a free EU research area by integrating the new member states.

Call for proposal

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Avenue Jean-Baptiste Clement 99

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