The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Universal measure zero, large Hausdorff dimension, and nearly Lipschitz maps”

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...

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. ...

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.

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.

Contracting-on-Average Baker Maps

Michał Rams (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

We estimate from above and below the Hausdorff dimension of SRB measure for contracting-on-average baker maps.