Adding machines, kneading maps, and endpoints
نویسندگان
چکیده
منابع مشابه
Kneading Theory for Triangular Maps
Abstract. The main purpose of this paper is to present a kneading theory for two-dimensional triangular maps. This is done by defining a tensor product between the polynomials and matrices corresponding to the one-dimensional basis map and fiber map. We also define a Markov partition by rectangles for the phase space of these maps. A direct consequence of these results is the rigorous computati...
متن کاملDynamics of continued fractions and kneading sequences of unimodal maps
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 کاملInfinite Kneading Matrices and Weighted Zeta Functions of Interval Maps
We consider a piecewise continuous, piecewise monotone interval map and a weight of bounded variation, constant on homtervals and continuous at periodic points of the map. With these data we associate a sequence of weighted Milnor-Thurston kneading matrices, converging to a countable matrix with coeecients analytic functions. We show that the determinants of these matrices converge to the inver...
متن کاملSharp Determinants and Kneading Operators for Holomorphic Maps
In an earlier paper 1] two of us studied generalized transfer operators M associated to maps of intervals of R. In particular the analyticity of a sharp determinant Det # (1?zM) was analyzed on the basis of spectral properties of M and by relating Det # (1 ? zM) to the determinant of 1 + D(z) for a suitable kneading operator D(z). It is a natural idea to try to replace monotone maps of interval...
متن کاملStrange 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.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2011
ISSN: 0166-8641
DOI: 10.1016/j.topol.2010.12.005