Search results for "Fractal set"

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Derivatives not first return integrable on a fractal set

2018

We extend to s-dimensional fractal sets the notion of first return integral (Definition 5) and we prove that there are s-derivatives not s-first return integrable.

Pure mathematicss-dimensional Hausdorff measureIntegrable systemApplied MathematicsGeneral MathematicsNumerical analysis010102 general mathematicss-setFirst return integrals-derivative01 natural sciences010305 fluids & plasmasSettore MAT/05 - Analisi Matematica0103 physical sciencesFractal set0101 mathematicsAlgebra over a fieldHenstock–Kurzweil integralMathematics
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Geometric rigidity of a class of fractal sets

2017

We study geometric rigidity of a class of fractals, which is slightly larger than the collection of self-conformal sets. Namely, using a new method, we shall prove that a set of this class is contained in a smooth submanifold or is totally spread out. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Set (abstract data type)Class (set theory)Pure mathematicsIterated function systemFractalGeneral MathematicsFOS: MathematicsRigidity (psychology)Fractal setDynamical Systems (math.DS)Mathematics - Dynamical SystemsSubmanifoldMathematicsMathematische Nachrichten
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