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 کاملWeighted kneading theory of one-dimensional maps with a hole
The purpose of this paper is to present a weighted kneading theory for one-dimensional maps with a hole. We consider extensions of the kneading theory of Milnor and Thurston to expanding discontinuous maps with a hole and introduce weights in the formal power series. This method allows us to derive techniques to compute explicitly the topological entropy, the Hausdorff dimension, and the escape...
متن کاملWeighted Kneading Theory of Unidimensional Maps with Holes
Abstract. The purpose of this paper is to present a weighted kneading theory for unidimensional maps with holes. We consider extensions of the kneading theory of Milnor and Thurston to expanding discontinuous maps with holes and introduce weights in the formal power series. This method allows us to derive techniques to compute explicitly the topological entropy, the Hausdorff dimension and the ...
متن کاملKneading Theory for a Family of Circle Maps with One Discontinuity
(3) F (x+ 1) = F (x) + 1 for all x ∈ R. For a map F ∈ C and for each a ∈ Z we set F (a) = limx↓a F (x) and F (a) = limx↑a F (x). In view of (3) we have F (a ) = F (0) + a and F (a) = F (0) + a. Note that the exact value of F (0) is not specified. Then in what follows we consider that F (0) is either F (0) or F (0−), or both, as necessary. Since every map F ∈ C has a discontinuity in each intege...
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...
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ژورنال
عنوان ژورنال: Banach Center Publications
سال: 1989
ISSN: 0137-6934,1730-6299
DOI: 10.4064/-23-1-83-89