Displaying similar documents to “Hausdorff dimensions in Engel expansions”

On the Hausdorff dimension of a family of self-similar sets with complicated overlaps

Balázs Bárány (2009)

Fundamenta Mathematicae

Similarity:

We investigate the properties of the Hausdorff dimension of the attractor of the iterated function system (IFS) {γx,λx,λx+1}. Since two maps have the same fixed point, there are very complicated overlaps, and it is not possible to directly apply known techniques. We give a formula for the Hausdorff dimension of the attractor for Lebesgue almost all parameters (γ,λ), γ < λ. This result only holds for almost all parameters: we find a dense set of parameters (γ,λ) for which the Hausdorff...

The growth rate and dimension theory of beta-expansions

Simon Baker (2012)

Fundamenta Mathematicae

Similarity:

In a recent paper of Feng and Sidorov they show that for β ∈ (1,(1+√5)/2) the set of β-expansions grows exponentially for every x ∈ (0,1/(β-1)). In this paper we study this growth rate further. We also consider the set of β-expansions from a dimension theory perspective.

Hausdorff gaps and towers in 𝓟(ω)/Fin

Piotr Borodulin-Nadzieja, David Chodounský (2015)

Fundamenta Mathematicae

Similarity:

We define and study two classes of uncountable ⊆*-chains: Hausdorff towers and Suslin towers. We discuss their existence in various models of set theory. Some of the results and methods are used to provide examples of indestructible gaps not equivalent to a Hausdorff gap. We also indicate possible ways of developing a structure theory for towers based on classification of their Tukey types.

Hausdorff operator on Morrey spaces and Campanato spaces

Jianmiao Ruan, Dashan Fan, Hongliang Li (2020)

Czechoslovak Mathematical Journal

Similarity:

We study the high-dimensional Hausdorff operators on the Morrey space and on the Campanato space. We establish their sharp boundedness on these spaces. Particularly, our results solve an open question posted by E. Liflyand (2013).

Perturbations of isometries between C(K)-spaces

Yves Dutrieux, Nigel J. Kalton (2005)

Studia Mathematica

Similarity:

We study the Gromov-Hausdorff and Kadets distances between C(K)-spaces and their quotients. We prove that if the Gromov-Hausdorff distance between C(K) and C(L) is less than 1/16 then K and L are homeomorphic. If the Kadets distance is less than one, and K and L are metrizable, then C(K) and C(L) are linearly isomorphic. For K and L countable, if C(L) has a subquotient which is close enough to C(K) in the Gromov-Hausdorff sense then K is homeomorphic to a clopen subset of L. ...

On the attractors of Feigenbaum maps

Guifeng Huang, Lidong Wang (2014)

Annales Polonici Mathematici

Similarity:

A solution of the Feigenbaum functional equation is called a Feigenbaum map. We investigate the likely limit set (i.e. the maximal attractor in the sense of Milnor) of a non-unimodal Feigenbaum map, prove that it is a minimal set that attracts almost all points, and then estimate its Hausdorff dimension. Finally, for every s ∈ (0,1), we construct a non-unimodal Feigenbaum map with a likely limit set whose Hausdorff dimension is s.

Separation conditions on controlled Moran constructions

Antti Käenmäki, Markku Vilppolainen (2008)

Fundamenta Mathematicae

Similarity:

It is well known that the open set condition and the positivity of the t-dimensional Hausdorff measure are equivalent on self-similar sets, where t is the zero of the topological pressure. We prove an analogous result for a class of Moran constructions and we study different kinds of Moran constructions in this respect.