View Proposal #190
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| ID | 190 |
|---|---|
| First Name | Marc |
| Last Name | Chamberland |
| Institution | Grinnell College |
| Speaker Category | faculty |
| Title of Talk | The Mean-Median Map |
| Abstract | Starting with a non-empty finite set S_n={x_1,\ldots,x_n} contained in R, generate the unique number x_{n+1} which satisfies the mean-median equation (x_1 + \cdots + x_n + x_{n+1}/(n+1) = median(S_n) . As usual, we define the median of the set S_n = {x_1,\ldots,x_n}, where x_1<= ... <= x_n, as median (S_n) = \left\{ x_{(n+1)/2}, n odd , \frac{x_{n/2} + x_{n/2+1}}{2}, n even . By applying the mean-median equation repeatedly to a set one generates an infinite sequence {x_k}_{k=1}^\infty. The dynamics of this map are surprising! Most maps tend to have either relatively simple dynamics or chaotic dynamics. While the mean-median map seems to be asymptotically constant, it seems very hard to predict. This talk will showcase the work done to date. This is joint work with Mario Martelli (Claremont McKenna College). |
| Subject area(s) | sequences, number theory, dynamics, fractals |
| Suitable for undergraduates? | Yes |
| Day Preference | |
| Computer Needed? | |
| Bringing a laptop? | Y |
| Overhead Needed? | N |
| Software requests | |
| Special Needs | |
| Date Submitted | 4/5/2007 |
| Year | 2007 |