Publications

I have authored a total of 8 and 48 , as listed below. This compilation also includes 7 and related works. My research primarily focuses on ergodic theory, fractal geometry, and geometric measure theory. Please be aware that the preprint versions may differ from the final published editions. Throughout my career, I have collaborated with 42 researchers, engaging in multiple projects with Balázs Bárány, Tapio Rajala, and Ville Suomala with whom I have worked at least five times each. Additionally, I have co-authored at least four papers with 6 researchers, at least three papers with 12 researchers, and at least two papers with 20 researchers. For more detailed bibliometric information, please refer to my MathSciNet profile, zbMATH Open profile, and Google Scholar profile.

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

  2. Regularity of non-autonomous self-similar sets
    (with A. Rutar)
    Preprint, 2024

  3. Thermodynamic formalism of countably generated self-affine sets
    (with I. D. Morris)
    Preprint, 2024

  4. Level sets of prevalent Hölder functions
    (with R. Anttila and B. Bárány)
    Proc. Amer. Math. Soc., to appear

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

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

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

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

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

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

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

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

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

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

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

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

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

  18. 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

  19. 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

  20. 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

  21. 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

  22. A Marstrand-type restricted projection theorem in R^3
    (with T. Orponen and L. Venieri)
    Amer. J. Math., to appear

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

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

  25. 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

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

  27. 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

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

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

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

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

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

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

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

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

  36. 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

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

  38. 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

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

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

  41. 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

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

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

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

  45. 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

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

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

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

  49. 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

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

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

  52. 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

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

  54. 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

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

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

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

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

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

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

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

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

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