Topological structures for periodic orbits of graph maps via suspension

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Project 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.

Original text from CORDIS.

Participants

• AUTONOMOUS UNIVERSITY OF BARCELONA · BELLATERRACoordinatorSpain

Links

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