Dynamical Systems, Graphs, Entropies, Dynamical Networks, and Statistical Mechanics

Series: 
Research Horizons Seminar
Wednesday, November 4, 2009 - 12:00
1 hour (actually 50 minutes)
Location: 
Skiles 171
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School of Mathematics, Georgia Tech
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Dynamical systems theory is concerned with systems that change in time (where time can be any semigroup). However, it is quite rare that one can find the solutions for such systems or even a "sizable" subset of such solutions. An approach motivated by this fact, that goes back to Poincaré, is to study instead partitions of the (phase) space M of all states of a dynamical system and consider the evolution of the elements of this partition (instead of the evolution of points of M). I'll explain how the objects in the title appear, some relations between them, and formulate a few general as well as more specific open problems suitable for a PhD thesis in dynamical systems, mathematical biology, graph theory and applied and computational mathematics. This talk will also serve to motivate and introduce to the topics to be given in tomorrow's colloquium.