Kneading sequences of strange adding machines
نویسندگان
چکیده
منابع مشابه
Strange Adding Machines
We show that given a type α of an adding machine, for a dense set of parameters s in the interval [ √ 2, 2], if f is the tent map with slope s, then the restriction of f to the closure of the orbit of the turning point is topologically conjugate to the adding machine map of type α.
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We introduce an invertible operation on finite sequences of positive integers and call it “kneading”. Kneading preserves three invariants of sequences — the parity of the length, the sum of the entries, and one we call the “alternant”. We provide a bijection between the set of sequences with alternant a and parity s and the set of Zagier-reduced indefinite binary quadratic forms with discrimina...
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In this paper we construct a correspondence between the parameter spaces of two families of one-dimensional dynamical systems, the α-continued fraction transformations Tα and unimodal maps. This correspondence identifies bifurcation parameters in the two families, and allows one to transfer topological and metric properties from one setting to the other. As an application, we recover results ab...
متن کاملComplexity of unimodal maps with aperiodic kneading sequences
It is well established that a formal language generated from a unimodal map is regular if and only if the map’s kneading sequence is either periodic or eventually periodic. A previously proposed conjecture said that if a language generated from a unimodal map is context-free, then it must be regular, i.e. there exists no proper context-free language which can be generated from a unimodal map. T...
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Hubbard trees are invariant trees connecting the points of the critical orbits of postcritically finite polynomials. Douady and Hubbard [DH1] introduced these trees and showed that they encode the essential information of Julia sets in a combinatorial way. The itinerary of the critical orbit within the Hubbard tree is encoded by a (pre)periodic sequence on {0, 1} called kneading sequence. We pr...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2009
ISSN: 0166-8641
DOI: 10.1016/j.topol.2008.11.018