For more information about this meeting, contact Stephen Simpson.
| Title: | How nicely can we tweak a nice map? |
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| Seminar: | Logic Seminar |
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| Speaker: | John Clemens, Pennsylvania State University, University of Muenster |
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| Abstract: |
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| The odometer map is defined on the Cantor space (the space
of all infinite sequences of 0's
and 1's) by adding 1 (mod 2) with carry to the right. This map has
been well-studied and has many nice
properties; for instance it admits a simple description as being
generated by a finite state automaton.
The orbits of the odometer turn out to be equivalence classes of the
relation E0 of eventual agreement
of sequences, with one exception: the eventually 0 sequences and the
eventually 1 sequences comprise
a single orbit.
We wish to determine how nice a map we can find whose orbits are
exactly the E0 classes, i.e., we wish
to nicely split the one exceptional orbit of the odometer into two
orbits. I will show how we can find a
homeomorphism of the Cantor space which generates E0; however, it
remains open whether we can
find a nicer map, such as an isometry or even one induced by an
automaton. I will discuss this question,
and how we can eliminate maps with certain additional niceties. |
Room Reservation Information
| Room Number: | MB315 |
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| Date: | 07 / 12 / 2011 |
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| Time: | 09:45am - 11:00am |
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