Pawel Pilarczyk: Automatic combinatorial-topological analysis of dynamical systems |
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Csütörtök, 26. Június 2014, 10:00 - 12:00
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| Abstract. A computational framework will be introduced for the combinatorial and topological analysis of discrete-time (semi)dynamical systems with parameters, or continuous-time dynamical systems (flows) by means of the analysis of the time-1 map. The main idea in this approach is to subdivide the space into compact subsets with disjoint interiors (a grid), and to represent the map by means of a multivalued mapping of grid elements. Graph algorithms allow to efficiently identify isolating neighborhoods that contain all the recurrent dynamics present in the system. The algebraic-topological invariant known as the Conley index provides reliable information on the dynamics in these neighborhoods. Interval arithmetic is involved in the numerics. These methods provide mathematically rigorous information on the system (a.k.a. computer-assisted proof). |
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Hely : Farkas terem, Bolyai Intézet |
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