New perspectives in the dimension theory of fractals

Research output

Research output per year 2021 2021 2022 2023 2024

• 33 Article
• 1 Conference contribution
• 1 Comment/debate

Research output per year

Research output per year

Search results

• 2024

  A new perspective on the Sullivan dictionary via Assouad type dimensions and spectra

  Fraser, J. & Stuart, L., 1 Jan 2024, In: Bulletin of the American Mathematical Society. 61, 1, p. 103-118 16 p.

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

  Open Access

  File

  • Parabolic 100%
  • Rational Map 100%
  • Dimension Theory 50%
  • Hyperbolic Space 50%
  • Julia Set 50%

• Assouad type dimensions of infinitely generated self-conformal sets

  Banaji, A. & Fraser, J., Apr 2024, In: Nonlinearity. 37, 4, 32 p., 045004.

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

  Open Access

  File

  • Limit Set 100%
  • Self-Conformal Set 100%
  • Parabolic 50%
  • Complex Number 50%
  • Dimension Theory 50%

• Assouad-type dimensions of overlapping self-affine sets

  Fraser, J. & Rutar, A., 11 Jan 2024, In: Annales Fennici Mathematici. 49, 1, p. 3-21

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

  Open Access

  File

  • Self-Affine Set 100%
  • Dimension Theory 14%
  • Maximal Dimension 14%
  • Set Satisfying 14%
  • Assouad Dimension 14%

• The Fourier spectrum and sumset type problems

  Fraser, J., 5 Apr 2024, In: Mathematische Annalen.

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

  Open Access

  File

  • Convolution 100%
  • Set Satisfying 100%
  • Hausdorff Dimension 100%
• 2023

  A nonlinear projection theorem for Assouad dimension and applications

  Fraser, J., 1 Feb 2023, In: Journal of the London Mathematical Society. 107, 2, p. 777-797 21 p.

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

  Open Access

  File

  • Projection Theorem 100%
  • Assouad Dimension 100%
  • Sharp Estimate 40%
  • Product Sum 20%
  • Orthogonal Projection 20%

• Box dimensions of (×m,×n)-invariant sets

  Fraser, J. & Jurga, N. A., 1 Dec 2023, In: Indiana University Mathematics Journal. 72, 6, p. 2341-2367 27 p.

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

  Open Access

  File

  • Box Dimension 100%
  • Invariant Set 100%
  • Subshift 83%
  • Lower and upper bounds 33%
  • Upper Bound 33%

• Dimensions of Kleinian orbital sets

  Bartlett, T. & Fraser, J., 6 Oct 2023, In: Journal of Fractal Geometry. 10, 3/4, p. 267-278 12 p.

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

  Open Access

  File

  • Box Dimension 100%
  • Fractal 33%
  • Hyperbolic Space 33%
  • Euclidean Space 33%
  • Limit Set 33%

• Dimensions of popcorn-like pyramid sets

  Banaji, A. & Chen, H., 10 Apr 2023, In: Journal of Fractal Geometry. 10, 1, p. 151-168 18 p.

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

  Open Access

  File

  • Box Dimension 100%
  • Dimension Theory 33%
  • Assouad Dimension 33%
  • Diophantine Approximation 33%
  • Probability Theory 33%

• Diophantine approximation in metric space

  Fraser, J., Koivusalo, H. & Ramirez, F., 1 Apr 2023, In: Bulletin of the London Mathematical Society. 55, 2, p. 756-776 21 p.

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

  Open Access

  File

  • Diophantine Approximation 100%
  • Metric Space 100%
  • Real Number 33%

• Generalised intermediate dimensions

  Banaji, A., 1 Nov 2023, In: Monatshefte für Mathematik. 202, 3, p. 465-506 42 p.

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

  Open Access

  File

  • Box Dimension 100%
  • Hausdorff Dimension 66%
  • Distribution Mass 33%
  • Relative Size 33%
  • Wide Class 33%

• Intermediate dimensions of infinitely generated attractors

  Banaji, A. & Fraser, J., 1 Apr 2023, In: Transactions of the American Mathematical Society. 376, 4, p. 2449-2479 31 p.

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

  Open Access

  File

  • Limit Set 100%
  • Box Dimension 50%
  • Hausdorff 50%
  • Iterated Function System 50%
  • Hausdorff Dimension 50%

• Metric spaces where geodesics are never unique

  Banaji, A., 1 Aug 2023, In: The American Mathematical Monthly. 130, 8, p. 747-754 8 p.

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

  Open Access

  File

  • Metric Space 100%
  • Normed Space 66%
  • Distinct Point 33%

• Minkowski dimension for measures

  Falconer, K. J., Fraser, J. & Käenmäki, A., 1 Feb 2023, In: Proceedings of the American Mathematical Society. 151, 2, p. 779-794 16 p.

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

  Open Access

  File

  • Minkowski Dimension 100%
  • Dimension Theory 66%
  • Box Dimension 33%
  • Compact Metric Space 33%

• On the convergence rate of the chaos game

  Bárány, B., Jurga, N. & Kolossváry, I., 1 Mar 2023, In: International Mathematics Research Notices. 2023, 5, p. 4456-4500 45 p., rnab370.

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

  Open Access

  File

  • Minkowski Dimension 100%
  • Convergence Rate 100%
  • Bernoulli Process 50%
  • Multiplicative 50%
  • Probability Vector 50%

• Refined horoball counting and conformal measure for Kleinian group actions

  Fraser, J. & Stuart, L., 8 May 2023, In: Annales Academiae Scientiarum Fennicae-Mathematica. 48, 1, p. 325-344 20 p.

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

  Open Access

  File

  • Parabolic 100%
  • Limit Set 75%
  • Fixed Points 50%
  • Countable Dense Subset 25%
  • Fractal Dimension 25%

• The L^q spectrum of self-affine measures on sponges

  Kolossvary, I. T., 1 Aug 2023, In: Journal of the London Mathematical Society. 108, 2, p. 666-701 36 p., 12767.

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

  Open Access

  File

  • Box Dimension 100%
  • Pressure Function 50%
  • Linear Part 50%
  • Upper Bound 50%
  • Closed Form 50%
• 2022

  An upper bound for the intermediate dimensions of Bedford–McMullen carpets

  Kolossváry, I., 11 Jul 2022, In: Journal of Fractal Geometry. 9, 1-2, p. 151-169 19 p.

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

  Open Access

  File

  • Upper Bound 100%
  • Box Dimension 100%
  • Hausdorff Dimension 66%

• Dimensions of the popcorn graph

  Chen, H., Fraser, J. & Yu, H., 18 Aug 2022, (E-pub ahead of print) In: Proceedings of the American Mathematical Society. 150, p. 4729-4742

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

  Open Access

  File

  • Box Dimension 100%
  • Assouad Dimension 100%
  • Diophantine Approximation 100%
  • Probability Theory 100%
  • Real Analysis 100%

• Distance between natural numbers based on their prime signature

  Kolossváry, I. B. & Kolossváry, I. T., May 2022, In: Journal of Number Theory. 234, p. 120-139

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

  Open Access

  File

  • Natural Number 100%
  • Random Variable 66%
  • Number Line 66%
  • Asymptotics 33%
  • Prime Number Theorem 33%

• Distance between natural numbers based on their prime signature

  Kolossváry, I. B. & Kolossváry, I. T., May 2022, In: Journal of Number Theory. 234, p. 120-139

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

  Open Access

  File

  • Natural Number 100%
  • Random Variable 50%
  • Number Line 50%
  • Prime Number 25%
  • Asymptotics 25%

• On the Fourier dimension of (d,k)-sets and Kakeya sets with restricted directions

  Fraser, J., Harris, T. L. J. & Kroon, N. G., 24 Feb 2022, (E-pub ahead of print) In: Mathematische Zeitschrift. First Online, 12 p.

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

  Open Access

  File

  • Unit Ball 100%
  • Hausdorff Dimension 50%

• Parabolic carpets

  Fraser, J. & Jurga, N. A., 9 Nov 2022, (Accepted/In press) In: Israel Journal of Mathematics.

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

  • Parabolic 100%
  • Box Dimension 25%
  • Fixed Points 25%
  • Gibbs Free Energy 25%
  • Iterated Function System 25%

• The Assouad dimension of self-affine measures on sponges

  Fraser, J. & Kolossvary, I. T., 8 Sept 2022, (E-pub ahead of print) In: Ergodic Theory and Dynamical Systems. FirstView, 23 p.

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

  Open Access

  File

  • Assouad Dimension 100%
  • Lower and upper bounds 40%
  • Coincides 40%
  • Explicit Formula 20%
  • Diagonalmatrix 20%

• The Assouad spectrum of Kleinian limit sets and Patterson-Sullivan measure

  Fraser, J. & Stuart, L., 10 Oct 2022, In: Geometriae Dedicata. 217, 32 p., 1.

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

  Open Access

  File

  • Box Dimension 100%
  • Assouad Dimension 100%
  • Patterson 100%
  • Limit Set 100%
  • Parabolic 25%

• The fractal structure of elliptical polynomial spirals

  Burrell, S. A., Falconer, K. J. & Fraser, J., 1 Sept 2022, In: Monatshefte für Mathematik. 199, p. 1-22

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

  Open Access

  File

  • Fractal 100%
  • Spiral 100%
  • Polynomial 100%
  • Fractional Brownian Motion 100%
  • Dimensional Analysis 100%

• The Poincaré exponent and the dimensions of Kleinian limit sets

  Fraser, J. M., 2022, In: The American Mathematical Monthly. 129, 5, p. 480-484 5 p.

  Research output: Contribution to journal › Comment/debate › peer-review

  Open Access

  File

  • Limit Set 100%
  • Fractal 25%
  • Box Dimension 25%
  • Hyperbolic Space 25%
  • Fractal Geometry 25%
• 2021

  Approximate arithmetic structure in large sets of integers

  Fraser, J. & Yu, H., 2021, In: Real Analysis Exchange. 46, 1, p. 163-174

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

  Open Access

  File

  • Integer 100%
  • Approximates 100%
  • Arithmetic Progression 50%

• Assouad dimension influences the box and packing dimensions of orthogonal projections

  Falconer, K. J., Fraser, J. & Shmerkin, P., 2021, In: Journal of Fractal Geometry. 8, 3, p. 247–259

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

  Open Access

  File

  • Box Dimension 100%
  • Assouad Dimension 100%
  • Orthogonal Projection 100%
  • Packing Dimension 100%
  • Dimensional Subspace 20%

• Fractal geometry of Bedford-McMullen carpets

  Fraser, J. M., 2021, Thermodynamic Formalism: CIRM Jean-Morlet Chair, Fall 2019. Pollicott, M. & Vaienti, S. (eds.). Springer, p. 495-516 22 p. (Lecture Notes in Mathematics; vol. 2290).

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

  Open Access

  File

  • Fractal Geometry 100%
  • Dimension Theory 50%
  • Self-Affine Set 50%

• Hausdorff measure and Assouad dimension of generic self-conformal IFS on the line

  Bárány, B., Simon, K., Kolossvary, I. T. & Rams, M., Dec 2021, In: Proceedings of the Royal Society of Edinburgh, Section A: Mathematics. 151, 6, p. 2051 - 2081 31 p.

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

  Open Access

  File

  • Assouad Dimension 100%
  • Hausdorff Measure 100%
  • Iterated Function System 100%
  • Transversals 25%
  • Real Line 25%

• Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions

  Fraser, J., Shmerkin, P. & Yavicoli, A., 10 Feb 2021, In: Journal of Fourier Analysis and Applications. 27, 4, 14 p., 4.

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

  Open Access

  File

  • Approximates 100%
  • Arithmetic Progression 100%
  • Hausdorff Dimension 100%
  • Real Line 50%
  • Box Dimension 50%

• L^q-spectra of measures on planar non-conformal attractors

  Falconer, K. J., Fraser, J. & Lee, L. D., Nov 2021, In: Ergodic Theory and Dynamical Systems. 41, 11, p. 3288-3306 19 p.

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

  Open Access

  File

  • Pressure Function 100%
  • Singular Value 100%
  • Bernoulli Process 100%
  • Lower Triangular Matrix 100%
  • Iterated Function System 100%

• On Hölder maps and prime gaps

  Chen, H. & Fraser, J., 8 Nov 2021, In: Real Analysis Exchange. 46, 2, p. 523-532

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

  Open Access

  File

  • Positive Integer 100%
  • Hlder Continuity 100%

• On Hölder solutions to the spiral winding problem

  Fraser, J., 7 May 2021, In: Nonlinearity. 34, 5, p. 3251–3270 20 p.

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

  Open Access

  File

  • Spiral 100%
  • Polynomial 33%
  • Dimension Theory 16%
  • Box Dimension 16%
  • Assouad Dimension 16%

• Regularity versus smoothness of measures

  Fraser, J. & Troscheit, S., 31 Jul 2021, In: Pacific Journal of Mathematics. 311, 2, p. 257–275 17 p.

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

  Open Access

  File

  • Continuous Measure 100%
  • Regular Measure 100%