Weighted kneading theory of one-dimensional maps with a hole
نویسندگان
چکیده
منابع مشابه
Weighted 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 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 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 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 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: International Journal of Mathematics and Mathematical Sciences
سال: 2004
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s016117120430428x