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Relations between Words and Maps of the Interval
James D.Louck1 and Myron L.Stein2
1T-Division, MS B210, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
jimlouck@lanl.gov
2TSA-Division, MS F602, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
mstein@lanl.gov
Annals of Combinatorics 5 (3) p.425-449 September, 2001
AMS Subject Classification: 37B10, 37C25, 37E05
Abstract:
Words on two letters may be used to label the inverse graph of the graph of the n-th iterate of the parabolic map of the interval, as well as general unimodal maps. What is interesting about this correspondence is the manner in which abstract properties of words imply, or control, corresponding properties of the functions constituting the inverse graph. We illustrate this by examples and give general theorems on the words that label the inverse graphs that undergo tangent and period-doubling bifurcations.
Keywords: maps of the interval, words, inverse parabolic map, bifurcation events, cycles

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