Root
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Conference Proceedings
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6th EUROMECH Nonlinear Dynamics Conference (ENOC 2008)
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On the application of a linear programming method to the
evaluation of the entropy of a symbolic image
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Entropy is one of the most important characteristics of the behavior of a dynamical system. For direct calculation both topological and metric entropy involves problems, the development of numerical methods of their estimation is the question of great importance. We use the concept of symbolic image, which is a finite approximation of a

dynamical system. Symbolic image is constructed as an oriented graph for a mapping $f$ and a fixed covering of its phase space. The vertices of the graph correspond to the cells of the covering and edges show the existence of nonempty intersections of the covering cells with their images. We use a method of linear programming, which allows us to construct an invariant measure on the

graph and thereby to specify a stationary process. The estimation of the entropy of such a process gives a bound for the entropy of $f.$

dynamical system. Symbolic image is constructed as an oriented graph for a mapping $f$ and a fixed covering of its phase space. The vertices of the graph correspond to the cells of the covering and edges show the existence of nonempty intersections of the covering cells with their images. We use a method of linear programming, which allows us to construct an invariant measure on the

graph and thereby to specify a stationary process. The estimation of the entropy of such a process gives a bound for the entropy of $f.$