Asymmetric tent map expansions II. Purely periodic points
نویسندگان
چکیده
منابع مشابه
Purely Periodic Β-expansions in the Pisot Non-unit Case
It is well known that real numbers with a purely periodic decimal expansion are rationals having, when reduced, a denominator coprime with 10. The aim of this paper is to extend this result to betaexpansions with a Pisot base beta which is not necessarily a unit. We characterize real numbers having a purely periodic expansion in such a base. This characterization is given in terms of an explici...
متن کاملPurely Periodic β-Expansions with Pisot Unit Bases over Laurent Series
The present paper deals with β-expansions in algebraic function fields. If β is a Pisot unit, we characterise the elements whose β-expansion is purely periodic. In order to pursue this characterisation, we introduce a variant of the Rauzy fractal.
متن کاملBoundary of Central Tiles Associated with Pisot Beta-numeration and Purely Periodic Expansions
This paper studies tilings related to the β-transformation when β is a Pisot number (that is not supposed to be a unit). Then it applies the obtained results to study the set of rational numbers having a purely periodic β-expansion. Secial focus is given to some quadratic examples.
متن کاملDynamical properties of the tent map
where β = β(β−1)−1, M ∈ N∪{∞}, and l0, l1, . . . is a uniquely determined (finite or infinite) sequence of non-negative integers (cf. [2]). Analogously to other types of expansions we may ask for bases β such that the set of numbers with periodic or even finite representation is as large as possible. In particular, we say that Tβ satisfies the periodicity property (P) if the orbit (T β (x))n≥1 ...
متن کاملOn the Barycenter of the Tent Map
It is well known that the average position or barycenter of generic orbits for the standard tent map is 0.5. Periodic orbits are exceptional orbits in the sense that most of them have barycenters different from 0.5. In this paper we prove that for any positive integer n, there exist n distinct periodic orbits for the standard tent map with the same barycenter. We also provide some patterns of p...
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: Illinois Journal of Mathematics
سال: 1994
ISSN: 0019-2082
DOI: 10.1215/ijm/1256060993