Jonathan Fraser

Search results

• 2018

  On The L^q dimensions of measures on Heuter-Lalley type self-affine sets

  Fraser, J. M. & Kempton, T., Jan 2018, In: Proceedings of the American Mathematical Society. 146, 1, p. 161-173

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

  Open Access

  File

  • Self-Affine Set 100%
  • Wide Class 25%
  • Theoretic Approach 25%
  • Hausdorff Dimension 25%
  • Considered Class 25%

• Quantifying inhomogeneity in fractal sets

  Fraser, J. & Todd, M. J., Apr 2018, In: Nonlinearity. 31, 4, p. 1313-1330

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

  Open Access

  File

  • Fractal Set 100%
  • Box Dimension 50%
  • Large Deviation Principle 50%
  • Scaling Behavior 50%
  • Assouad Dimension 50%

• The Assouad dimension of randomly generated fractals

  Fraser, J. M., Miao, J. J. & Troscheit, S., May 2018, In: Ergodic Theory and Dynamical Systems. 38, 3, p. 982-1011

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

  Open Access

  File

  • Fractal 100%
  • Assouad Dimension 100%
  • Topological Structure 33%
  • Theoretic Structure 33%
  • Packing Dimension 33%
• 2017

  Assouad type dimensions for self-affine sponges

  Fraser, J. M. & Howroyd, D. C., 2017, In: Annales Academiae Scientiarum Fennicae-Mathematica. 42, p. 149-174 42.

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

  Open Access

  • Regularity Property 100%
  • Doubling Measure 100%

• Dimensions of sets which uniformly avoid arithmetic progressions

  Fraser, J. M., Saito, K. & Yu, H., 2 Nov 2017, (E-pub ahead of print) In: International Mathematics Research Notices. 2017, 12 p.

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

  Open Access

  File

  • Arithmetic Progression 100%
  • Hausdorff Dimension 28%
  • Upper Bound 14%
  • Approximates 14%
  • Main Result 14%

• Some results in support of the Kakeya conjecture

  Fraser, J. M., Olson, E. & Robinson, J., 1 Oct 2017, In: Real Analysis Exchange. 42, 2, p. 253-268

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

  Open Access

  File

  • Besicovitch 100%
  • Box-Counting Dimension 40%
  • Line Segment 40%
  • Assouad Dimension 20%

• The Assouad dimension of self-affine carpets with no grid structure

  Fraser, J. M. & Jordan, T., 16 Jun 2017, In: Proceedings of the American Mathematical Society. 145, p. 4905-4918

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

  Open Access

  File

  • Assouad Dimension 100%
  • Local Dimension 33%
  • Self-Affine Set 33%
  • Bernoulli Process 16%
  • Box Dimension 16%

• The Assouad dimensions of projections of planar sets

  Fraser, J. M. & Orponen, T., Feb 2017, In: Proceedings of the London Mathematical Society. 114, 2, p. 374-398 25 p.

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

  Open Access

  File

  • Assouad Dimension 100%
  • Hausdorff Dimension 40%
  • Self-Similar Set 30%
  • Hausdorff Measure 20%
  • Projection Theorem 10%

• Uniform scaling limits for ergodic measures

  Fraser, J. M. & Pollicott, M., 2017, In: Journal of Fractal Geometry. 4, 1, p. 1-19

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

  Open Access

  File

  • Scaling Limit 100%
  • Ergodic Measure 100%
  • Statistical Property 50%
  • Common Distribution 50%
  • Gibbs Free Energy 50%
• 2016

  Inhomogeneous self-affine carpets

  Fraser, J. M., 2016, In: Indiana University Mathematics Journal. 65, p. 1547-1566

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

  • Dimension Theory 100%
  • Box Dimension 100%
  • Self-Similar Set 50%

• On the dimensions of a family of overlapping self-affine carpets

  Fraser, J. M. & Shmerkin, P., Dec 2016, In: Ergodic Theory and Dynamical Systems. 36, 8, p. 2463–2481

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

  Open Access

  File

  • Small Set 100%
  • Box Dimension 100%
  • Translation Vector 100%
  • Packing Dimension 100%
  • Hausdorff Dimension 100%

• On the L^q -spectrum of planar self-affine measures

  Fraser, J. M., 2016, In: Transactions of the American Mathematical Society. 368, 8, p. 5579-5620 42 p.

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

  Open Access

  File

  • Singular Value 100%
  • Dimension Theory 100%
  • Closed Form 100%
  • Differentiability 100%
  • Bernoulli Process 100%
• 2015

  A note on the 1-prevalence of continuous images with full Hausdorff dimension

  Fraser, J. M. & Hyde, J. T., 2015, In: Journal of Mathematical Analysis and Applications. 421, 2, p. 1713-1720 8 p.

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

• Dimension and measure for typical random fractals

  Fraser, J. M., 2015, In: Ergodic Theory and Dynamical Systems. 35, 3, p. 854-882 29 p.

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

• First and second moments for self-similar couplings and Wasserstein distances

  Fraser, J. M., 2015, In: Mathematische Nachrichten. 288, p. 2028-2041.

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

  • Wasserstein Distance 100%
  • Self-Similar Measure 50%
  • Integral 50%
  • Lower and upper bounds 25%
  • Product Space 25%

• Micromeasure distributions and applications for conformally generated fractals

  Fraser, J. M. & Pollicott, M., 2015, In: Mathematical Proceedings of the Cambridge Philosophical Society. 159, 3, p. 547-566 20 p.

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

• On the Assouad dimension of self-similar sets with overlaps

  Fraser, J. M., Henderson, A. M., Olson, E. J. & Robinson, J. C., 19 Mar 2015, In: Advances in Mathematics. 273, p. 188-214 27 p.

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

  • Assouad Dimension 100%
  • Self-Similar Set 100%
  • Hausdorff Dimension 50%
  • Approximates 25%
  • Main Result 25%

• On the equality of Hausdorff measure and Hausdorff content

  Farkas, Á. & Fraser, J. M., 2015, In: Journal of Fractal Geometry. 2, 4, p. 403-429 27 p.

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

• Remarks on the analyticity of subadditive pressure for products of triangular matrices

  Fraser, J. M., 2015, In: Monatshefte für Mathematik. 177, 1, p. 53-65 13 p.

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

• Scaling scenery of (x m, x n) invariant measures

  Ferguson, A., Fraser, J. M. & Sahlsten, T., 2 Jan 2015, In: Advances in Mathematics. 268, p. 564-602 39 p.

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

  • Bernoulli Process 100%
  • Invariant Measure 100%
  • Toral Endomorphism 50%
  • Fractal 50%
  • Projection Theorem 50%

• Sixty years of fractal projections

  Falconer, K. J., Fraser, J. M. & Jin, X., 31 Jul 2015, Fractal Geometry and Stochastics V. Bandt, C., Falconer, K. J. & Zähle, M. (eds.). Basel: Birkhauser, p. 3-25 23 p. (Progress in Probability; vol. 70).

  Research output: Chapter in Book/Report/Conference proceeding › Chapter

  Open Access

  File

  • Fractal 100%
  • Marstrand 100%
  • Projection Theorem 50%
  • Fractal Geometry 50%
  • Orthogonal Projection 50%
• 2014

  Assouad type dimensions and homogeneity of fractals

  Fraser, J. M., Dec 2014, In: Transactions of the American Mathematical Society. 366, 12, p. 6687-6733 47 p.

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

  Open Access

  File

  • Fractal 100%
  • Assouad Dimension 100%
  • Hausdorff Dimension 100%
  • Self-Affine Set 100%
  • Self-Similar Set 100%

• On Fourier analytic properties of graphs

  Fraser, J. M., Orponen, T. & Sahlsten, T., 2014, In: International Mathematics Research Notices. 2014, 10, p. 2730-2745 16 p.

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

  • Real Valued Function 100%
  • Unit Interval 100%
  • Fractional Brownian Motion 100%
• 2013

  Dimension and measure for generic continuous images

  Balka, R., Farkas, A., Fraser, J. M. & Hyde, J. T., 2013, In: Annales Academiae Scientiarum Fennicae-Mathematica. 38, 1, p. 389-404 16 p.

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

  Open Access

  File

  • Continuous Image 100%
  • Topological Dimension 100%
  • Box Dimension 66%
  • Compact Metric Space 66%
  • Continuous Function 66%

• The visible part of plane self-similar sets

  Falconer, K. J. & Fraser, J. M., 2013, In: Proceedings of the American Mathematical Society. 141, 1, p. 269-278

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

  Open Access

  File

  • Half line 100%
  • Intersects 100%
  • Convex Open Set 100%
  • Open Set Condition 100%
  • Hausdorff Dimension 100%
• 2012

  Inhomogeneous self-similar sets and box dimensions

  Fraser, J. M., 2012, In: Studia Mathematica. 213, 2, p. 133-156 24 p.

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

• On the packing dimension of box-like self-affine sets in the plane

  Fraser, J. M., 15 Jun 2012, In: Nonlinearity. 25, 7, p. 2075-2092 18 p.

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

  • Packing Dimension 100%
  • Self-Affine Set 100%
  • Iterated Function System 66%
  • Singular Value 33%
  • Open Set Condition 33%
• 2011

  Multifractal spectra of random self-affine multifractal Sierpinski sponges in ℝ^d

  Fraser, J. M. & Olsen, L. O. R., 2011, In: Indiana University Mathematics Journal. 60, 3, p. 937-984 48 p.

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

• The Hausdorff dimension of graphs of prevalent continuous functions

  Fraser, J. M. & Hyde, J. T., 2011, In: Real Analysis Exchange. 37, 2, p. 333-351 19 p.

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

• The horizon problem for prevalent surfaces

  Falconer, K. J. & Fraser, J. M., 2011, In: Mathematical Proceedings of the Cambridge Philosophical Society. 151, 2, p. 355-372 18 p.

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

  Open Access

  File

  • Box Dimension 100%
  • Horizon Problem 100%
  • Fractal Surface 16%