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TOPOLOGICAL STRUCTURES FOR PERIODIC ORBITS OF GRAPH MAPS VIA SUSPENSION |
| Host Laboratory | Scientific Supervisor | |
| Universitat Autonoma de Barcelona Departamento de Matematicas - Facultad de Ciencias EDIFICI CC 08193 Barcelona Spain |
MR. Lluis Alseda I Soler Tel : 34/35812539 / Fax : 34/35812790 Email : alseda@mat.uab.es | |
| Grant Holder | ||
| Dr. Francois Gautero (French) Tel : 33/493896830 / Fax : | ||
| Abstract Research objectives and content The proposed research program is 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 program is 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 program to be developped since the dynamical system group is very active, as well as the Algebraic topology group. Contract number : FMBICT983176 | ||
Last updated :10:07:98
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