The Geometry Of Fractal Sets

By S. Pfeifer. 2016

582 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/32c8cb82f5b4903f89030a343cb0a7cba003ed99

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Citations in the corpus

Finite chains inside thin subsets of ℝd (2014, methodology): “[6], [17] or [11] ) we may take μ to satisfy the same properties as in the statement of Theorem 1.”
Metric Diophantine Approximation : aspects of recent work (2016, background): “Clearly, it can easily be adapted to the setting of arbitrary metric spaces – see [49, 71].”
On the Assouad dimension of self-similar sets with overlaps (2014, background): “It is well known, see for example Edgar [6] or Falconer [7], that there exists a unique non-empty compact set F ⊆ R satisfying”
Sixty years of fractal projections (2014, background): “For a both broader and more detailed coverage of various aspects of projections, the books by Falconer [16, 17] and Mattila [58, 62] and the survey articles by Mattila [59, 60, 61] may be helpful.”
Geometric properties of the Markov and Lagrange spectra (2016, background): “(See [Fal86] for the deﬁnitions and basic properties of the notions of dimension used in this paper.)”
Assouad Dimension and Fractal Geometry (2020, background): “7.1 Self-similar sets and the Hutchinson-Moran formula 96 7.2 The Assouad dimension of self-similar sets 98 7.3 The Assouad spectrum of self-similar sets 106 7.4 Dimensions of self-similar measures 109 8 Self-affine sets 113 8.1 Self-affine sets and two strands of research 113 8.2 Falconer’s formula”
On the differentiability of Lipschitz functions with respect to measures in the Euclidean space (2014, background): “Thus I ′ must have measure 0.(10) Statement (vi).”
Hausdorff dimension of the graphs of the classical Weierstrass functions (2015, background): “plies that the Hausdorﬀ dimension is at least D. On the other hand, it is easy to check that f is a C2−D function which implies that the Hausdorﬀ dimension is at most D(see for example Theorem 8.1 of [5]). 6.1. Telescope. Deﬁne Φ : [0,1)×R→ [0,1)×Ras Φ(x,y) = (bx mod 1,(y−φ(x))/λ). Deﬁne G: [0,1)×R×”