Adding machines.




Jones, Leslie Braziel.

Access rights

Worldwide access

Journal Title

Journal ISSN

Volume Title



We explore the endpoint structure of the inverse limit space of unimodal maps such that the restriction of the map to the ω-limit set of the critical point is topologically conjugate to an adding machine. These maps fall into the infinitely renormalizable unimodal family or the family of strange adding machines. A unimodal map, f, is renormalizable if there exists a restrictive interval J in its domain of period n such that J contains the critical point and fn : J → J is a unimodal map. If the renomalization process can be repeated infinitely often, we have an infinitely renormalizable map. Strange adding machines, however, are not renormalizable, and understanding the dynamical differences in these two families of maps is one of our goals. We give a characterization of the kneading sequence structure for these strange adding machines, and use this characterization to provide an example of a strange adding machine for which the set of folding points and the set of endpoints are not equal in the inverse limit space. We show that in the case of infinitely renormalizable maps, these two sets will always coincide. We extend our endpoint result by considering maps on finite graphs.


Includes bibliographical references (p. 66-68).


Calculators., Mapping (Mathematics), Topological spaces., Topological dynamics.