Corpus ID: 119174349

$L^q$-spectra of self-affine measures: closed forms, counterexamples, and split binomial sums

@article{Fraser2018LqspectraOS,
  title={\$L^q\$-spectra of self-affine measures: closed forms, counterexamples, and split binomial sums},
  author={Jonathan M. Fraser and L. Lee and I. Morris and Han Yu},
  journal={arXiv: Metric Geometry},
  year={2018}
}
  • Jonathan M. Fraser, L. Lee, +1 author Han Yu
  • Published 2018
  • Mathematics
  • arXiv: Metric Geometry
  • We study $L^q$-spectra of planar self-affine measures generated by diagonal systems with an emphasis on providing closed form expressions. We answer a question posed by Fraser in 2016 in the negative by proving that a certain natural closed form expression does not generally give the $L^q$-spectrum and, using a similar approach, find counterexamples to a statement of Falconer-Miao from 2007 and a conjecture of Miao from 2008 concerning a closed form expression for the generalised dimensions of… CONTINUE READING

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    References

    SHOWING 1-10 OF 13 REFERENCES
    The geometry of self-affine fractals
    • 2
    • Highly Influential
    • PDF
    A dimension result arising from the ^{}-spectrum of a measure
    • 57
    • PDF
    A Class of Self-Affine Sets and Self-Affine Measures
    • 58
    • PDF
    Generalized dimensions of measures on self-affine sets
    • 41
    • PDF
    On the packing dimension of box-like self-affine sets in the plane
    • 48
    • PDF
    A Multifractal Formalism
    • 333
    Multifractal Formalism for Almost all Self-Affine Measures
    • 25
    • PDF
    On the $L^q$-spectrum of planar self-affine measures
    • 9
    • PDF
    DIMENSIONS OF SELF-AFFINE FRACTALS AND MULTIFRACTALS GENERATED BY UPPER-TRIANGULAR MATRICES
    • 43
    • Highly Influential
    • PDF