Search results for "28D05"

showing 2 items of 2 documents

On a normal form of symmetric maps of [0, 1]

1980

A class of continuous symmetric mappings of [0, 1] into itself is considered leaving invariant a measure absolutely continuous with respect to the Lebesgue measure.

Discrete mathematicsPure mathematicsLebesgue measureLebesgue's number lemmaStatistical and Nonlinear Physics58F20Absolute continuityLebesgue integrationLebesgue–Stieltjes integrationsymbols.namesakeNonlinear system28D05symbolsInvariant (mathematics)Borel measureMathematical PhysicsMathematicsCommunications in Mathematical Physics
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Weak separation condition, Assouad dimension, and Furstenberg homogeneity

2015

We consider dimensional properties of limit sets of Moran constructions satisfying the finite clustering property. Just to name a few, such limit sets include self-conformal sets satisfying the weak separation condition and certain sub-self-affine sets. In addition to dimension results for the limit set, we manage to express the Assouad dimension of any closed subset of a self-conformal set by means of the Hausdorff dimension. As an interesting consequence of this, we show that a Furstenberg homogeneous self-similar set in the real line satisfies the weak separation condition. We also exhibit a self-similar set which satisfies the open set condition but fails to be Furstenberg homogeneous.

General MathematicsHomogeneity (statistics)ta111Open setPrimary 28A80 Secondary 37C45 28D05 28A50Moran constructioniterated function systemSet (abstract data type)CombinatoricsDimension (vector space)dimensionMathematics - Classical Analysis and ODEsweak separation conditionClassical Analysis and ODEs (math.CA)FOS: MathematicsLimit (mathematics)Limit setCluster analysisReal lineMathematics
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