Publications

I have authored , across 29 journals, and along with related works, as detailed below. My research focuses on , , and . I have collaborated with 46 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 7 researchers, three papers with 12, and two papers with 22. For comprehensive bibliometric details, consult my MathSciNet, zbMATH Open, and Google Scholar profiles.

  1. Rational points of exact period three for the quadratic family
    (with P. Kosunen)
    Preprint, 2026

  2. Exponential separation of self-conformal systems
    Preprint, 2026

  3. Projections of self-affine sets onto lines
    (with B. Bárány and I. Kolossváry)
    Preprint, 2026

  4. On the Marstrand projection theorem for the Assouad spectrum
    (with K. J. Falconer and J. M. Fraser)
    Preprint, 2026

  5. Level sets of prevalent Weierstrass functions
    (with Z. Buczolich and B. Maga)
    J. Lond. Math. Soc., to appear

  6. Self-affine sponges with random contractions
    (with B. Bárány and M. Rams)
    Probab. Theory Related Fields, to appear

  7. Tangents and slices of self-affine carpets
    (with A. Rutar)
    Ergodic Theory Dynam. Systems, to appear

  8. Regularity of non-autonomous self-similar sets
    (with A. Rutar)
    Math. Proc. Cambridge Philos. Soc., 179 (2025), no. 3, 623-648

  9. Thermodynamic formalism of countably generated self-affine sets
    (with I. D. Morris)
    Trans. Amer. Math. Soc., 379 (2026), no. 5, 3161-3210

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

  11. Local dimension spectrum for dominated planar self-affine sets
    (with A. Batsis and T. Kempton)
    Math. Z., 312 (2026), no. 4, Paper No. 115

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

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

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

  15. Covering number on inhomogeneous graph-directed self-similar sets
    (with B. Bárány and P. Nissinen)
    J. Fractal Geom., 13 (2026), no. 3-4, 241-262

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

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

  18. Finer geometry of planar self-affine sets
    (with B. Bárány and H. Yu)
    Adv. Math., 493 (2026), Paper No. 110914

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

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

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

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

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

  24. 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

  25. 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

  26. 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

  27. 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

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

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

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

  31. 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

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

  33. 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

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

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

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

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

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

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

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

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

  42. 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

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

  44. 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

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

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

  47. 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

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

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

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

  51. 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

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

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

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

  55. 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

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

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

  58. 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

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

  60. 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

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

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

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

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

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

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

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

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

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