Topology Proceedings 30 No. 1 (2006), pp. 39-58

Continuous Itinerary Functions on Dendroids

Stewart Baldwin

It is well known that most of the information about the dynamics of a unimodal interval map can be obtained from its "kneading sequence" (the itinerary of its turning point with respect to the map), and similar results are known for trees and dendrites having exactly one "turning point" (a point where the function is not locally one-to-one). We show here that these ideas can be extended to a large class of unimodal dendroid maps (with an appropriate extension of the term "unimodal") satisfying the unique itinerary property, and provide a routine method for constructing many examples of such maps. In this case, the basic invariants are the kneading sequence and a zero-dimensional compact Hausdorff space which tells how the various components of D\{t} limit on each other (where t is the "turning point").

Keywords: combinatorial dynamics, dendrite, dendroid, itinerary, unimodal map

Mathematics Subject Classification: 37E15 37E25 54F15

Document formats: PDF file 227.0 Kb

Topology Proceedings, Volume 30, No. 1 (2006)
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