The Relative Growth of Information in Two-Dimensional Partitions.
Connections for Women: Dynamical Systems
January 17,2007 11:30 AM to 12:00 PM
Speakers:
Johnson, Aimee
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Summary: |
The problem of finding information about a continued fraction expansion from the first n digits of the decimal expansion is recast in terms of a measureable dynamical system. Using partitions and entropy the same result as found previously is uncovered in a more general setting. |
Abstract: |
In a 1964 paper, Lochs considered how much knowledge the first n digits in the decimal expansion of a number from the unit interval would give about the digits in its continued fraction expansion, and showed that for a.e. x, the limiting behavior of these two numbers of digits is always the same. In this talk, we will recast this problem in terms of measurable dynamical systems and see how using partitions and entropy lead to the same result and in fact, let us put the result in a more general framework. Finally we will consider how the dynamics and geometry change when we consider points from the unit square. |
Keywords: |
Loch; Entropy; Ergodic System; Information. |
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Lecture #13230
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• Aimee.ppt (0.3 MB)
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