Publications

I have authored , across 28 journals, and along with related works, as detailed below. My research focuses on , , and . I have collaborated with 44 researchers, notably with Balázs Bárány, Tapio Rajala, and Ville Suomala, each on at least five projects. Additionally, I have co-authored at least four papers with 6 researchers, three papers with 12, and two papers with 21. For comprehensive bibliometric details, consult my MathSciNet, zbMATH Open, and Google Scholar profiles.

  1. Level sets of prevalent Weierstrass functions
    (with Z. Buczolich and B. Maga)
    Preprint, 2025

  2. Self-affine sponges with random contractions
    (with B. Bárány and M. Rams)
    Preprint, 2025

  3. Tangents and slices of self-affine carpets
    (with A. Rutar)
    Preprint, 2024

  4. Regularity of non-autonomous self-similar sets
    (with A. Rutar)
    Math. Proc. Cambridge Philos. Soc., to appear

  5. Thermodynamic formalism of countably generated self-affine sets
    (with I. D. Morris)
    Trans. Amer. Math. Soc., to appear

  6. Level sets of prevalent Hölder functions
    (with R. Anttila and B. Bárány)
    Proc. Amer. Math. Soc., 153 (2025), no. 5, 2023-2035

  7. Local dimension spectrum for dominated irreducible planar self-affine sets
    (with A. Batsis and T. Kempton)
    Preprint, 2024

  8. Tangents of invariant sets
    (with A. Rutar)
    Preprint, 2023

  9. Scaling limits of self-conformal measures
    (with B. Bárány, A. Pyörälä, and M. Wu)
    Preprint, 2023

  10. Dimension of planar non-conformal attractors with triangular derivative matrices
    (with B. Bárány)
    Comm. Math. Phys., 405 (2024), no. 11, Paper No. 256

  11. Covering number on inhomogeneous graph-directed self-similar sets
    (with B. Bárány and P. Nissinen)
    Preprint, 2023

  12. Slices of the Takagi function
    (with R. Anttila and B. Bárány)
    Ergodic Theory Dynam. Systems, 44 (2024), no. 9, 2361-2398

  13. Non-invertible planar self-affine sets
    (with P. Nissinen)
    Math. Proc. Cambridge Philos. Soc., 177 (2024), no. 1, 49-65

  14. Finer geometry of planar self-affine sets
    (with B. Bárány and H. Yu)
    Preprint, 2021

  15. Minkowski dimension for measures
    (with K. J. Falconer and J. M. Fraser)
    Proc. Amer. Math. Soc., 151 (2023), no. 2, 779-794

  16. Super-exponential condensation without exact overlaps | Numerical calculations
    (with B. Bárány)
    Adv. Math., 379 (2021), Paper No. 107549

  17. Assouad dimension of planar self-affine sets
    (with B. Bárány and E. Rossi)
    Trans. Amer. Math. Soc., 374 (2021), no. 2, 1297-1326

  18. Absolute continuity in families of parametrised non-homogeneous self-similar measures
    (with T. Orponen)
    J. Fractal Geom., 10 (2023), no. 1, 169-207

  19. Attainable values for the Assouad dimension of projections
    (with J. M. Fraser)
    Proc. Amer. Math. Soc., 148 (2020), no. 8, 3393-3405

  20. On the Hausdorff dimension of microsets
    (with J. M. Fraser, D. C. Howroyd, and H. Yu)
    Proc. Amer. Math. Soc., 147 (2019), no. 11, 4921-4936

  21. Birkhoff and Lyapunov spectra on planar self-affine sets
    (with B. Bárány, T. Jordan, and M. Rams)
    Int. Math. Res. Not., IMRN 2021, no. 10, 7966-8005

  22. Self-conformal sets with positive Hausdorff measure | Numerical calculations
    (with J. Angelevska and S. Troscheit)
    Bull. Lond. Math. Soc., 52 (2020), no. 1, 200-223

  23. Domination, almost additivity, and thermodynamic formalism for planar matrix cocycles
    (with B. Bárány and I. D. Morris)
    Israel J. Math., 239 (2020), no. 1, 173-214

  24. A Marstrand-type restricted projection theorem in R^3
    (with T. Orponen and L. Venieri)
    Amer. J. Math., 147 (2025), no. 1, 81-123

  25. Dynamics of the scenery flow and conical density theorems
    Banach Center Publ., 115 (2018), 99-143

  26. Self-affine sets in analytic curves and algebraic surfaces
    (with D.-J. Feng)
    Ann. Acad. Sci. Fenn. Math., 43 (2018), no. 1, 109-119

  27. Dimension of self-affine sets for fixed translation vectors
    (with B. Bárány and H. Koivusalo)
    J. Lond. Math. Soc., 98 (2018), no. 1, 223-252

  28. Genericity of dimension drop on self-affine sets
    (with B. Li)
    Statist. Probab. Lett., 126 (2017), 18-25

  29. Structure of equilibrium states on self-affine sets and strict monotonicity of affinity dimension
    (with I. D. Morris)
    Proc. Lond. Math. Soc., 116 (2018), no. 4, 929-956

  30. Measures with predetermined regularity and inhomogeneous self-similar sets
    (with J. Lehrbäck)
    Ark. Mat., 55 (2017), no. 1, 165-184

  31. Rigidity of quasisymmetric mappings on self-affine carpets
    (with T. Ojala and E. Rossi)
    Int. Math. Res. Not., IMRN 2018, no. 12, 3769-3799

  32. A note on correlation and local dimensions
    (with J. Yang and M. Wu)
    Chaos Solitons Fractals, 97 (2017), 39-43

  33. Ledrappier-Young formula and exact dimensionality of self-affine measures
    (with B. Bárány)
    Adv. Math., 318 (2017), 88-129

  34. Weak separation condition, Assouad dimension, and Furstenberg homogeneity
    (with E. Rossi)
    Ann. Acad. Sci. Fenn. Math., 41 (2016), no. 1, 465-490

  35. Self-affine sets with fibered tangents
    (with H. Koivusalo and E. Rossi)
    Ergodic Theory Dynam. Systems, 37 (2017), no. 6, 1915-1934

  36. Local dimensions in Moran constructions
    (with B. Li and V. Suomala)
    Nonlinearity, 29 (2016), no. 3, 807-822

  37. Scenery flow, conical densities, and rectifiability
    Fractal Geometry and Stochastics V, Springer International Publishing, 2015, 27-38

  38. Dynamics of the scenery flow and geometry of measures
    (with T. Sahlsten and P. Shmerkin)
    Proc. Lond. Math. Soc., 110 (2015), no. 5, 1248-1280

  39. Structure of distributions generated by the scenery flow
    (with T. Sahlsten and P. Shmerkin)
    J. Lond. Math. Soc., 91 (2015), no. 2, 464-494

  40. Multifractal analysis of Birkhoff averages for typical infinitely generated self-affine sets
    (with H. W. J. Reeve)
    J. Fractal Geom., 1 (2014), no. 1, 83-152

  41. Dimensions, Whitney covers, and tubular neighborhoods
    (with J. Lehrbäck and M. Vuorinen)
    Indiana Univ. Math. J., 62 (2013), no. 6, 1861-1889

  42. Local conical dimensions for measures
    (with D.-J. Feng and V. Suomala)
    Math. Proc. Cambridge Philos. Soc., 154 (2013), no. 3, 465-479

  43. Dimensions of random affine code tree fractals
    (with E. Järvenpää, M. Järvenpää, H. Koivusalo, Ö. Stenflo, and V. Suomala)
    Ergodic Theory Dynam. Systems, 34 (2014), no. 3, 854-875

  44. Local structure of self-affine sets
    (with C. Bandt)
    Ergodic Theory Dynam. Systems, 33 (2013), no. 5, 1326-1337

  45. Existence of doubling measures via generalised nested cubes
    (with T. Rajala and V. Suomala)
    Proc. Amer. Math. Soc., 140 (2012), no. 9, 3275-3281

  46. Local multifractal analysis in metric spaces
    (with T. Rajala and V. Suomala)
    Nonlinearity, 26 (2013), no. 8, 2157-2173

  47. Local homogeneity and dimensions of measures
    (with T. Rajala and V. Suomala)
    Ann. Sc. Norm. Super. Pisa Cl. Sci., 16 (2016), no. 4, 1315-1351

  48. Equilibrium states for the pressure function for products of matrices
    (with D.-J. Feng)
    Discrete Contin. Dyn. Syst., 30 (2011), no. 3, 699-704

  49. Dimension and measures on sub-self-affine sets
    (with M. Vilppolainen)
    Monatsh. Math., 161 (2010), no. 3, 271-293

  50. On upper conical density results
    Recent Developments in Fractals and Related Fields, Applied and Numerical Harmonic Analysis, 2010, 45-54

  51. Upper conical density results for general measures on R^n
    (with M. Csörnyei, T. Rajala, and V. Suomala)
    Proc. Edinburgh Math. Soc., 53 (2010), no. 2, 311-331

  52. Itseaffiineista joukoista
    Arkhimedes, (2008), no. 2, 17-20

  53. Porosity and regularity in metric measure spaces
    Real Anal. Exchange 2007, 31st Summer Symposium Conference, 245-250

  54. Packing dimension and Ahlfors regularity of porous sets in metric spaces
    (with E. Järvenpää, M. Järvenpää, T. Rajala, S. Rogovin, and V. Suomala)
    Math. Z., 266 (2010), no. 1, 83-105

  55. Overlapping self-affine sets of Kakeya type
    (with P. Shmerkin)
    Ergodic Theory Dynam. Systems, 29 (2009), no. 3, 941-965

  56. Packing dimension of mean porous measures
    (with D. Beliaev, E. Järvenpää, M. Järvenpää, T. Rajala, S. Smirnov, and V. Suomala)
    J. Lond. Math. Soc., 80 (2009), no. 2, 514-530

  57. Separation conditions on controlled Moran constructions
    (with M. Vilppolainen)
    Fund. Math., 200 (2008), no. 1, 69-100

  58. Conical upper density theorems and porosity of measures
    (with V. Suomala)
    Adv. Math., 217 (2008), no. 3, 952-966

  59. Geometric rigidity of a class of fractal sets
    Math. Nachr., 279 (2006), no. 1-2, 179-187

  60. Asymptotically sharp dimension estimates for k-porous sets
    (with E. Järvenpää, M. Järvenpää, and V. Suomala)
    Math. Scand., 97 (2005), no. 2, 309-318

  61. Measures of full dimension on self-affine sets
    Acta Univ. Carolin. Math. Phys., 45 (2004), no. 2, 45-53

  62. Nonsymmetric conical upper density and k-porosity
    (with V. Suomala)
    Trans. Amer. Math. Soc., 363 (2011), no. 3, 1183-1195

  63. Iterated function systems: Natural measure and local structure
    Rep. Univ. Jyväskylä Dept. Math. Stat., 93 (2003)

  64. On natural invariant measures on generalised iterated function systems
    Ann. Acad. Sci. Fenn. Math., 29 (2004), no. 2, 419-458

  65. On the geometric structure of the limit set of conformal iterated function systems
    Publ. Mat., 47 (2003), no. 1, 133-141