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M. Howard Lee - Physics Department, University of Georgia

As a prototypical 1d chaotic map, the logistic map has played an
important role in elucidating the chaotic behavior in nature. By
necessity nearly all the studies on this map have been numerical and
numerically driven.  It has been found recently that the dynamical
behavior of 3-cycles in this map can actually be studied analytically.*
There is a new theorem by a Ukrainian mathematician A Sharkovskii,
according to which the existence of a 3-cycle implies the existence of
all other cycles. Thus there exists chaos. The dynamical behavior of the
logistic map will be discussed at an introductory level. Implications of
chaos to statistical mechanics will also be brought up.

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* M H Lee, J. Math. Phys. (Dec. 2009)