6533b82bfe1ef96bd128d6d4

RESEARCH PRODUCT

Local multifractal analysis in metric spaces

Ville SuomalaAntti KäenmäkiTapio Rajala

subject

Pure mathematicsApplied MathematicsGeneral Physics and AstronomyMetric Geometry (math.MG)Statistical and Nonlinear PhysicsDynamical Systems (math.DS)Multifractal systemType (model theory)28A80 28D20 54E50Metric spaceLocal spectrumMathematics - Metric GeometryMathematics - Classical Analysis and ODEsClassical Analysis and ODEs (math.CA)FOS: MathematicsMathematics - Dynamical SystemsMathematical PhysicsMathematics

description

We study the local dimensions and local multifractal properties of measures on doubling metric spaces. Our aim is twofold. On one hand, we show that there are plenty of multifractal type measures in all metric spaces which satisfy only mild regularity conditions. On the other hand, we consider a local spectrum that can be used to gain finer information on the local behaviour of measures than its global counterpart.

yearjournalcountryeditionlanguage
2013-06-26Nonlinearity
https://doi.org/10.1088/0951-7715/26/8/2157