Objective
Research objectives and content
The proposed research programmeis to understand some structures for the set of periodic orbits for continuous maps of a graph into itself. The goal is to give a general framework where all the previously known cases would be included. Some particular cases have been intensively studied '` la Sharkovskii', such as the interval circle and tree maps. The case of surface homeomorphisms has been treated via special graph maps and should also be a particular case. The new ingredient in this programmeis to consider graph maps via the 'suspension operation' for which I gave a combinatorial construction in my PhD thesis. This operation gives at the same time a 2-dimensional complex and a semi-flow. A periodic orbit of a graph map gives rise to both an element of the fundamental group of this complex and a periodic orbit of the semi-flow. The initial dynamical problem can then be studied by standard Algebraic technics and, for instance, a generalization of the notion of 'braid type' is expected. Training content (objective, benel it and expected impact)
Barcelona is a perfect place for such a programmeto be developped since the dynamical system group is very active, as well as the Algebraic topology group.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics applied mathematics dynamical systems
- natural sciences mathematics pure mathematics topology algebraic topology
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Programme(s)
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Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
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Funding Scheme
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Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Coordinator
08193 BELLATERRA
Spain
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