Prof Lars Olsen

Professor

Researcher profile

Phone

+44 (0)1334 46 3437

Email

lo@st-andrews.ac.uk

Office

203 MI

Location

Mathematical Institute

 

Research areas

Fractal geometry, dynamical systems, analysis

Roughly speaking, fractals are objects with detail at arbitrarily fine scales under increased magnification a fractal displays more and more intricate structure. New techniques of fractal geometry have enabled fractals to be analysed - it is a great challenge to develop mathematics suitable for describing and analysing objects of such a general and irregular nature.

Recently, multifractals have attracted great interest. A multifractal is a distribution that gives rise to a whole hierarchy of fractals, and analysis of these fractals and calculation of a multifractal spectrum tells us much about the distribution. Again, multifractals have been used to model physical phenomena, for example the energy dissipation across a turbulent fluid.

PhD supervision

• Luke Derry

Selected publications

• Open access

  Average frequencies of digits in infinite IFS’s and applications to continued fractions and Lüroth expansions

  Olsen, L. & West, M., 12 Aug 2020, (E-pub ahead of print) In: Monatshefte für Mathematik. First Online, 38 p.

  Research output: Contribution to journal › Article › peer-review

• Open access

  On exponential densities and limit ratios of subsets of N

  Li, J. & Olsen, L., 28 Jun 2020, In: Mediterranean Journal of Mathematics. 17, 17 p., 122.

  Research output: Contribution to journal › Article › peer-review

• Open access

  On average Hewitt-Stromberg measures of typical compact metric spaces

  Olsen, L., 24 Jan 2019, (E-pub ahead of print) In: Mathematische Zeitschrift. First Online, 25 p.

  Research output: Contribution to journal › Article › peer-review

• Open access

  On the rate of convergence of ((||ƒ||_p)¦(||ƒ||∞))^p as p →∞

  Olsen, L. O. R., Feb 2019, In: Mediterranean Journal of Mathematics. 16, 10 p., 11.

  Research output: Contribution to journal › Article › peer-review

• Open access

  Average distances between points in graph-directed self-similar fractals

  Olsen, L. & Richardson, A., 27 Aug 2018, (E-pub ahead of print) In: Mathematische Nachrichten. Early View, 25 p.

  Research output: Contribution to journal › Article › peer-review

• Open access

  On the Hausdorff and packing measures of typical compact metric spaces

  Jurina, S., MacGregor, N., Mitchell, A., Olsen, L. & Stylianou, A., Aug 2018, In: Aequationes Mathematicae. 92, 4, p. 709–735 27 p.

  Research output: Contribution to journal › Article › peer-review

• Open access

  On the average L^q-dimensions of typical measures belonging to the Gromov-Hausdorff-Prohoroff space

  Olsen, L., 27 Sept 2018, (E-pub ahead of print) In: Journal of Mathematical Analysis and Applications. In press

  Research output: Contribution to journal › Article › peer-review

• Open access

  On the average box dimensions of graphs of typical continuous functions

  Adam-Day, B., Ashcroft, C., Olsen, L., Pinzani, N., Rizzoli, A. & Rowe, J., Dec 2018, In: Acta Mathematica Hungarica. 156, 2, p. 263-302 40 p.

  Research output: Contribution to journal › Article › peer-review

• Open access

  On the Π⁰_γ-completeness and Σ⁰_γ-completeness of multifractal decomposition sets

  Olsen, L. O. R., 2018, In: Mathematika. 64, 1, p. 77-114 38 p.

  Research output: Contribution to journal › Article › peer-review

• Open access

  Average distances on self-similar sets and higher order average distances of self-similar measures

  Allen, D., Edwards, H., Harper, S. & Olsen, L. O. R., Oct 2017, In: Mathematische Zeitschrift. 287, 1-2, p. 287-324 38 p.

  Research output: Contribution to journal › Article › peer-review

 

See more publications