June 26, 2007
The JSTOR database is an archive of important scholarly journals, offering researchers high-resolution, scanned images of journal issues and pages. It now includes 37,094 articles from The American Mathematical Monthly, from 1894 to 2003. The 1962 article "College Admissions and the Stability of Marriage" by David Gale and Lloyd Shapley ranks as the most frequently accessed Monthly article in the database. Second place goes to "Introduction to Fermat's Last Theorem" by David A. Cox. Third place belongs to "Period Three Implies Chaos" by Tien-Yien Li and James A. Yorke.
"Period Three Implies Chaos"
Tien-Yien Li and James A Yorke
The American Mathematical Monthly, Vol. 82, No. 10 (December, 1975), pp. 985-992
Chaos theory describes the behavior of certain nonlinear dynamical systems that under specific conditions exhibit dynamics that are sensitive to initial conditions. As a result of this sensitivity and an exponential growth of errors in the initial conditions, the behavior of chaotic systems appears to be random. Yorke coined the term chaos, as used in mathematics, and here, with Li, proves that any one-dimensional system that exhibits a regular cycle of period three will also display regular cycles of every other length, along with completely chaotic behavior.
Access to the JSTOR archive is provided by many college, university, and other libraries. To find out if your library is a JSTOR participant, use one of the following links:
United States: http://www.jstor.org/about/participants_na.html.
Other Countries: http://www.jstor.org/about/participants_intl.html.
If your library is not on one of the above lists, look for a nearby library that does have JSTOR access and is open to the public. Members of the MAA have the option of purchasing an individual subscription to JSTOR that gives them access to the archives of The American Mathematical Monthly, Mathematics Magazine, and The College Mathematics Journal.