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Complexity for symbolic dynamical systems

Contributed by Ted Galanthay on 02/24/21 

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Ever wondered about entropy and complexity?  Come to a talk by Andrew Dykstra from Hamilton College at 4pm on Monday, March 1, Zoom link

Andrew Dykstra will present on "Complexity for symbolic dynamical systems" at 4pm on Monday, March 1 on Zoom.

Abstract:In this talk, we will discuss dynamical systems that are symbolic in nature, meaning that points in the system are infinite sequences of symbols.  For example, the set of all possible infinite sequences of 0’s and 1’s, i.e., the set of all binary sequences, is a symbolic space which (as we will discuss) can be thought of as a dynamical system.  Whenever you have a symbolic dynamical system like this, it is natural to look for ways to measure how rich (or complicated) the system is.  One way of doing this is to calculate the entropy of a system. As we will see, even within the special class of systems that have entropy zero, it is still possible to distinguish among systems by measuring their complexity.  In particular, we will show how to use complexity to characterize important properties of systems such as recurrence, minimality, and transitivity.

Sponsored by the Math department colloquium series

Contact: Ted Galanthay, tgalanthay@ithaca.edu

 

 

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