DS-MINIM · Dynamics of Homeomorphisms, Noninvertible Maps and Flows with Respect to Minimality
FP6 — Marie Curie Actions (Human Resources and Mobility)
- Duration
- 2006-05-01 → 2008-04-30
- EU contribution
- €207,786
- Participants
- 1
- Scheme
- EIF
Lines connect the coordinator with its partners.
Results in brief
Final Activity Report Summary - DS-MINIM (Dynamics of Homeomorphisms, Noninvertible Maps and Flows with Respect to Minimality)
The project was focused on studying dynamical systems given by an action of a continuous map or homeomophism on a metric space with respect to minimality and related properties such as transitivity and aperiodicity. We constructed a new, rich class of minimal systems with dynamics given by a continuous map, almost totally disconnected dynamical systems, with complicated behaviour; we fully described minimal sets on these spaces and proved several others general results; as a consequence we got a full topological characterization of minimal sets on dendrites. We studied minimal sets of homeomorphisms on noncompact surfaces of finite type; we gave partial description of possible minimal sets in this setting; we constructed an example of embedded non-compact Cantor set as minimal set in this case. We studied fixed point free homeomorphisms of the open and closed annulus; we got partial results about the existence of foliations with free leaves. We studied almost periodically forced systems; we constructed an explicit example of embedded Denjoy dynamics in a system with no invariant curves; we proved other related results in this setting. Two non-equivalent definitions of minimality are discussed in a general setting; a panorama of old and new results of general character is presented.
Data: CORDIS, © European Union
Project objective
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.
Original text from CORDIS.
Participants
- UNIVERSITE PARIS 13 · VILLETANEUSECoordinatorFrance
Links
Data: CORDIS, © European Union