Attractor of Cantor Type with Positive Measure
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DOI: 10.1007/s00025-018-0828-3
Abstract: We construct an iterated function system consisting of strictly increasing contractions $$f,g:[0,1]\rightarrow [0,1]$$f,g:[0,1]→[0,1] with $$f([0,1])\cap g([0,1])=\emptyset $$f([0,1])∩g([0,1])=∅ and such that its attractor has positive Lebesgue measure. read more here.
Keywords: type positive; measure; cantor type; positive measure ... See more keywords
Spread of Values of a Cantor-Type Fractal Continuous Nonmonotone Function
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DOI: 10.1007/s10958-019-04356-0
Abstract: By using the Q5∗$$ {Q}_5^{\ast } $$-representation of numbers01∋x=βα1x1+∑k=2∞βαkxk∏j=1k−1qαjxj=Δα1xα2x…αkx…Q5∗$$ \left[0,1\right]\ni x={\beta}_{\alpha_1(x)1}+\sum \limits_{k=2}^{\infty}\left({\beta}_{\alpha_k(x)k}\prod \limits_{j=1}^{k-1}{q}_{\alpha_j(x)j}\right)={\Delta}_{\alpha_1(x){\alpha}_2(x)\dots {\alpha}_k(x)\dots}^{Q_5^{\ast }} $$determined by the quinary alphabet A5 ≡ {0, 1, 2, 3, 4} and an infinite stochastic matrix ‖qik‖, i ∈ A5, k ∈ N, with positive elements (q0k + q1k + q2k + q3k + q4k = 1) such that… read more here.
Keywords: alpha dots; alpha sum; delta; cantor type ... See more keywords