https://m2.mtmt.hu/ hun 2026-07-28 06:57 JournalArticle 30603311 VALIDATED true MTA-BME Stochastics Research Group, Department of Stochastics, Budapest University of Technology and Economics, P.O. Box 91, Budapest, 1521, Hungary Einstein Institute of Mathematics, Edmond J. Safra Campus (Givat Ram), The Hebrew University, Jerusalem, 91904, Israel Export Date: 25 September 2019 Correspondence Address: Hochman, M.; Einstein Institute of Mathematics, Edmond J. Safra Campus (Givat Ram), The Hebrew UniversityIsrael; email: mhochman@math.huji.ac.il MTA-BME Stochastics Research Group, Department of Stochastics, Budapest University of Technology and Economics, P.O. Box 91, Budapest, 1521, Hungary Einstein Institute of Mathematics, Edmond J. Safra Campus (Givat Ram), The Hebrew University, Jerusalem, 91904, Israel Cited By :18 Export Date: 22 September 2021 Correspondence Address: Hochman, M.; Einstein Institute of Mathematics, Israel; email: mhochman@math.huji.ac.il Funding details: Seventh Framework Programme, FP7, 306494 MTA-BME Stochastics Research Group, Department of Stochastics, Budapest University of Technology and Economics, P.O. Box 91, Budapest, 1521, Hungary Einstein Institute of Mathematics, Edmond J. Safra Campus (Givat Ram), The Hebrew University, Jerusalem, 91904, Israel Cited By :18 Export Date: 23 September 2021 Correspondence Address: Hochman, M.; Einstein Institute of Mathematics, Israel; email: mhochman@math.huji.ac.il Funding details: Seventh Framework Programme, FP7, 306494 0 false 2026-06-02T21:18:24.746+0000 2020-12-23T08:16:13.302+0000 2019-03-18T15:51:41.629+0000 true 10042216 Bárány Balázs /api/author/10042216 Author Bárány Balázs (sztochasztika) true 10042216 2025-04-07T03:48:50.656+0000 2020-01-08T20:18:54.993+0000 true 565 WoS import /api/admin/565 Admin WoS import (admin) true true false true 24 24 /api/publicationtype/24 PublicationType Folyóiratcikk 1 true 24 JournalArticle true 10000059 Article true 24 24 /api/publicationtype/24 PublicationType Folyóiratcikk 1 true 24 JournalArticle /api/subtype/10000059 Szakcikk SubType Szakcikk (Folyóiratcikk) 101 true 10000059 true 1 /api/category/1 Category Tudományos true 1 Bárány, Balázs true true /api/journal/2143 REVIEWED INVENTIONES MATHEMATICAE 0020-9910 1432-1297 true false 2143 false 2143 true 0020-9910 1432-1297 Journal FOREIGN 216 3 601 659 601 59 2019 true true 2019 true true true false true false NONE 2026-06-02 false 91 0 91 74 17 91 90 85 62 87 87 70 70 74 17 0 91 74 91 74 0 10 10 Folyóiratcikk Journal Article 24 86 Könyvrészlet Chapter in Book 25 3 Könyv Book 23 2 Egyéb konferenciaközlemény Conference paper 31 0 Egyéb konferenciakötet Conference proceedings 32 0 Oltalmi formák Protection forms 26 0 Disszertáció Thesis 28 0 Egyéb Miscellaneous 29 0 Alkotás Achievement 22 0 Kutatási adat Research data 33 0 Folyóiratcikk Journal Article 24 0 0 0 Könyvrészlet Chapter in Book 25 0 0 0 Könyv Book 23 0 0 0 Egyéb konferenciaközlemény Conference paper 31 0 0 0 Egyéb konferenciakötet Conference proceedings 32 0 0 0 Oltalmi formák Protection forms 26 0 0 0 Disszertáció Thesis 28 0 0 0 Egyéb Miscellaneous 29 0 0 0 Alkotás Achievement 22 0 0 0 Kutatási adat Research data 33 0 0 0 2018 0 2 1 2 1 2019 0 3 3 3 3 2020 0 7 6 7 6 2021 0 21 16 21 16 2022 0 10 9 10 9 2023 0 15 14 15 14 2024 0 15 11 15 11 2025 0 9 7 9 7 2026 0 9 7 9 7 D1 false 10042216 false false false 2019-06-16T14:51:53.951+0000 2019-03-18T15:51:54.132+0000 MTA-BME Sztochasztika Kutatócsoport (BME / TTK / MI / SZT); 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Arnold, L.: Random Dynamical Systems. Springer Monographs in Mathematics. Springer, Berlin (1998), DOI: 10.1007/978-3-662-12878-7 1 10.1007/978-3-662-12878-7 false true Reference 2467688 /api/reference/2467688 2. Barański, K.: Hausdorff dimension of the limit sets of some planar geometric constructions. Adv. Math. 210(1), 215–245 (2007), DOI: 10.1016/j.aim.2006.06.005 2 10.1016/j.aim.2006.06.005 false true Reference 2467689 /api/reference/2467689 3. Bárány, B.: On the Ledrappier–Young formula for self-affine measures. Math. Proc. Camb. Philos. Soc. 159(3), 405–432 (2015), DOI: 10.1017/S0305004115000419 3 10.1017/S0305004115000419 false true Reference 2467690 /api/reference/2467690 4. Bárány, B., Käenmäki, A.: Ledrappier–Young formula and exact dimensionality of self-affine measures. Adv. Math. 318, 88–129 (2017), DOI: 10.1016/j.aim.2017.07.015 4 10.1016/j.aim.2017.07.015 false true Reference 2467691 /api/reference/2467691 5. Bárány, B., Rams, M., Simon, K.: On the dimension of triangular self-affine sets (2016). arXiv preprint arXiv:1609.03914 5 false true Reference 2467692 /api/reference/2467692 6. Bedford, T.: The box dimension of self-affine graphs and repellers. Nonlinearity 2(1), 53 (1989), DOI: 10.1088/0951-7715/2/1/005 6 10.1088/0951-7715/2/1/005 false true Reference 2467693 /api/reference/2467693 7. Bougerol, P., Lacroix, J.: Products of random matrices with applications to Schrödinger operators. Progress in Probability and Statistics, vol. 8. Birkhäuser Boston Inc, Boston (1985) 7 false true Reference 2467694 /api/reference/2467694 8. Dysman, M.: Fractal dimensions for repellers of maps with holes. J. Stat. Phys. 120(3–4), 479–509 (2005), DOI: 10.1007/s10955-005-5964-y 8 10.1007/s10955-005-5964-y false true Reference 2467695 /api/reference/2467695 9. Falconer, K., Kempton, T.: Planar self-affine sets with equal Hausdorff, box and affinity dimensions. Ergod. Theory Dyn. Syst. 7 (2016) 9 false true Reference 2467696 /api/reference/2467696 10. Falconer, K., Kempton, T.: The dimension of projections of self-affine sets and measures. Ann. Acad. Sci. Fenn. Math. 42(1), 473–486 (2017), DOI: 10.5186/aasfm.2017.4232 10 10.5186/aasfm.2017.4232 false true Reference 2467697 /api/reference/2467697 11. Falconer, K., Miao, J.: Dimensions of self-affine fractals and multifractals generated by upper-triangular matrices. Fractals 15(3), 289–299 (2007), DOI: 10.1142/S0218348X07003587 11 10.1142/S0218348X07003587 false true Reference 2467698 /api/reference/2467698 12. Falconer, K.J.: The Hausdorff dimension of some fractals and attractors of overlapping construction. J. Stat. Phys. 47(1–2), 123–132 (1987), DOI: 10.1007/BF01009037 12 10.1007/BF01009037 false true Reference 2467699 /api/reference/2467699 13. Falconer, K.J.: The Hausdorff dimension of self-affine fractals. Math. Proc. Camb. Philos. Soc. 103(2), 339–350 (1988), DOI: 10.1017/S0305004100064926 13 10.1017/S0305004100064926 false true Reference 2467700 /api/reference/2467700 14. Falconer, K.J.: The dimension of self-affine fractals II. Math. Proc. Camb. Philos. Soc. 111(1), 169–179 (1992), DOI: 10.1017/S0305004100075253 14 10.1017/S0305004100075253 false true Reference 2467701 /api/reference/2467701 15. Fan, A.-H., Lau, K.-S., Rao, H.: Relationships between different dimensions of a measure. Monatsh. Math. 135(3), 191–201 (2002), DOI: 10.1007/s006050200016 15 10.1007/s006050200016 false true Reference 2467702 /api/reference/2467702 16. Fraser, J.M.: On the packing dimension of box-like self-affine sets in the plane. Nonlinearity 25(7), 2075 (2012), DOI: 10.1088/0951-7715/25/7/2075 16 10.1088/0951-7715/25/7/2075 false true Reference 2467703 /api/reference/2467703 17. Hochman, M.: On self-similar sets with overlaps and inverse theorems for entropy. Ann. Math. (2) 180(2), 773–822 (2014), DOI: 10.4007/annals.2014.180.2.7 17 10.4007/annals.2014.180.2.7 false true Reference 2467704 /api/reference/2467704 18. Hochman, M.: On self-similar sets with overlaps and inverse theorems for entropy in {\mathbb{R}}^d R d . Memoires of the AMS. (2015). To appear, available at arxiv:1503.09043 18 false true Reference 2467705 /api/reference/2467705 19. Hochman, M.: Some problems on the boundary of fractal geometry and additive combinatorics. In: Proceedings of FARF 3 (2017). To appear, available at arXiv:1608.02711 19 false true Reference 2467706 /api/reference/2467706 20. Hochman, M., Shmerkin, P.: Local entropy averages and projections of fractal measures. Ann. Math. (2) 175(3), 1001–1059 (2012), DOI: 10.4007/annals.2012.175.3.1 20 10.4007/annals.2012.175.3.1 false true Reference 2467707 /api/reference/2467707 21. Hueter, I., Lalley, S.P.: Falconer’s formula for the Hausdorff dimension of a self-affine set in { R}^2 R 2 . Ergod. Theory Dyn. Syst. 15(1), 77–97 (1995), DOI: 10.1017/S0143385700008257 21 10.1017/S0143385700008257 false true Reference 2467708 /api/reference/2467708 22. Hutchinson, J.E.: Fractals and self-similarity. Indiana Univ. Math. J. 30(5), 713–747 (1981), DOI: 10.1512/iumj.1981.30.30055 22 10.1512/iumj.1981.30.30055 false true Reference 2467709 /api/reference/2467709 23. Jordan, T., Pollicott, M., Simon, K.: Hausdorff dimension for randomly perturbed self affine attractors. Commun. Math. Phys. 270(2), 519–544 (2007), DOI: 10.1007/s00220-006-0161-7 23 10.1007/s00220-006-0161-7 false true Reference 2467710 /api/reference/2467710 24. Käenmäki, A.: Measures of full dimension on self-affine sets. Acta Univ. Carolin. Math. Phys. 45(2), 45–53 (2004). 32nd Winter School on Abstract Analysis 24 false true Reference 2467711 /api/reference/2467711 25. Käenmäki, A.: On natural invariant measures on generalised iterated function systems. Ann. Acad. Sci. Fenn. Math. 29(2), 419–458 (2004) 25 false true Reference 2467712 /api/reference/2467712 26. Käenmäki, A., Rajala, T., Suomala, V.: Existence of doubling measures via generalised nested cubes. Proc. Am. Math. Soc 140, 3275–3281 (2012), DOI: 10.1090/S0002-9939-2012-11161-X 26 10.1090/S0002-9939-2012-11161-X false true Reference 2467713 /api/reference/2467713 27. Käenmäki, A., Shmerkin, P.: Overlapping self-affine sets of Kakeya type. Ergod. Theory Dyn. Syst. 29(3), 941–965 (2009), DOI: 10.1017/S0143385708080474 27 10.1017/S0143385708080474 false true Reference 2467714 /api/reference/2467714 28. Kirat, I., Kocyigit, I.: A new class of exceptional self-affine fractals. J. Math. Anal. Appl. 401(1), 55–65 (2013), DOI: 10.1016/j.jmaa.2012.10.065 28 10.1016/j.jmaa.2012.10.065 false true Reference 2467715 /api/reference/2467715 29. Lalley, S.P., Gatzouras, D.: Hausdorff and box dimensions of certain self-affine fractals. Indiana Univ. Math. J. 41(2), 533–568 (1992), DOI: 10.1512/iumj.1992.41.41031 29 10.1512/iumj.1992.41.41031 false true Reference 2467716 /api/reference/2467716 30. Ledrappier, F.: On the dimension of some graphs. In: Symbolic dynamics and its applications (New Haven, CT, 1991), volume 135 of Contemporary Mathematics, pp. 285–293. American Mathematical Society, Providence (1992) 30 false true Reference 2467717 /api/reference/2467717 31. Mattila, P.: Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability, vol. 44 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge (1995), DOI: 10.1017/CBO9780511623813 31 10.1017/CBO9780511623813 false true Reference 2467718 /api/reference/2467718 32. McMullen, C.: The Hausdorff dimension of general Sierpiński carpets. Nagoya Math. J. 96, 1–9 (1984), DOI: 10.1017/S0027763000021085 32 10.1017/S0027763000021085 false true Reference 2467719 /api/reference/2467719 33. Morris, I.D., Shmerkin, P.: On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems. Trans. Amer. Math. Soc. 371, 1547–1582 (2019), DOI: 10.1090/tran/7334 33 10.1090/tran/7334 false true Reference 2467720 /api/reference/2467720 34. Persson, T.: On the Hausdorff dimension of piecewise hyperbolic attractors. Fund. Math. 207(3), 255–272 (2010), DOI: 10.4064/fm207-3-3 34 10.4064/fm207-3-3 false true Reference 2467721 /api/reference/2467721 35. Rams, M.: Absolute continuity of the SBR measure for non-linear fat baker maps. Nonlinearity 16(5), 1649–1655 (2003), DOI: 10.1088/0951-7715/16/5/306 35 10.1088/0951-7715/16/5/306 false true Reference 2467722 /api/reference/2467722 36. Rams, M., Simon, K.: Hausdorff and packing measure for solenoids. Ergod. Theory Dyn. Syst. 23(1), 273–291 (2003), DOI: 10.1017/S0143385702000883 36 10.1017/S0143385702000883 false true Reference 2467723 /api/reference/2467723 37. Rapaport, A.: On self-affine measures with equal Hausdorff and Lyapunov dimensions. Trans. Amer. Math. Soc. 370, 4759–4783 (2018), DOI: 10.1090/tran/7099 37 10.1090/tran/7099 false true Reference 2467724 /api/reference/2467724 38. Schmeling, J., Troubetzkoy, S.: Dimension and invertibility of hyperbolic endomorphisms with singularities. Ergod. Theory Dyn. Syst. 18(5), 1257–1282 (1998), DOI: 10.1017/S0143385798117996 38 10.1017/S0143385798117996 false true Reference 2467725 /api/reference/2467725 39. Simon, K.: Hausdorff dimension for non-invertible maps. Ergod. Theory Dyn. Syst. 13(1), 199–212 (1993), DOI: 10.1017/S014338570000729X 39 10.1017/S014338570000729X false true Reference 2467726 /api/reference/2467726 40. Solomyak, B.: Measure and dimension for some fractal families. Math. Proc. Camb. Philos. Soc. 124(3), 531–546 (1998), DOI: 10.1017/S0305004198002680 40 10.1017/S0305004198002680 false true Reference 2467727 /api/reference/2467727 41. Takagi, T.: A simple example of a continuous function without derivative. Proc. Phys. Math. Soc. Jpn. 1, 176–177 (1903) 41 false true Reference 2467728 /api/reference/2467728 42. Tsujii, M.: Fat solenoidal attractors. Nonlinearity 14(5), 1011–1027 (2001), DOI: 10.1088/0951-7715/14/5/306 42 10.1088/0951-7715/14/5/306 false true Reference 2467729 /api/reference/2467729 43. Varjú, P.: Absolute continuity of Bernoulli convolutions for algebraic parameters. Preprint (2016). http://arxiv.org/abs/1602.00261 43 false true Reference 2467730 /api/reference/2467730 44. Young, L.S.: Dimension, entropy and Lyapunov exponents. Ergod. Theory Dyn. Syst. 2(1), 109–124 (1982), DOI: 10.1017/S0143385700009615 44 10.1017/S0143385700009615 false true /api/publication/30603311 Bárány Balázs et al. Hausdorff dimension of planar self-affine sets and measures. (2019) INVENTIONES MATHEMATICAE 0020-9910 1432-1297 216 3 601-659<div class="JournalArticle Publication long-list"> <div class="authors"> <img title="Forrásközlemény" style="float: left" src="/frontend/resources/grid/publication-core-icon.png"> <img title="Idézőközlemény" style="float: left" src="/frontend/resources/grid/publication-citation-icon.png"> <div class="autype autype0"> <span class="author-name" mtid="10042216"><a href="/gui2/?type=authors&mode=browse&sel=10042216" target="_blank">Bárány Balázs (<span class="authorship-author-name">Bárány Balázs</span> <span class="authorAux-mtmt"> sztochasztika</span>) </a> </span> <span class="author-affil"><span title="Budapesti Műszaki és Gazdaságtudományi Egyetem">BME</span>/<span title="Természettudományi Kar">TTK</span>/<span title="Matematika Intézet">MI</span>/<span title="Sztochasztika Tanszék">SZT</span>/MTA-BME Sztochasztika Kutatócsoport; <span title="Budapesti Műszaki és Gazdaságtudományi Egyetem">BME</span>/<span title="Természettudományi Kar">TTK</span>/<span title="Matematika Intézet">MI</span>/Sztochasztika Tanszék</span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >Hochman Michael </span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >Rapaport Ariel </span> </div> </div> <div class="title"><a href="/gui2/?mode=browse&params=publication;30603311" target="_blank">Hausdorff dimension of planar self-affine sets and measures</a></div> <div> <span class="journal-title">INVENTIONES MATHEMATICAE</span> <span class="journal-issn">(<a target="_blank" href="https://portal.issn.org/resource/ISSN/0020-9910">0020-9910</a> <a target="_blank" href="https://portal.issn.org/resource/ISSN/1432-1297">1432-1297</a>)</span>: <span class="journal-volume">216</span> <span class="journal-issue">3</span> <span class="page"> pp 601-659 </span> <span class="year">(2019)</span> </div> <div class="pub-footer"> <span class="language" xmlns="http://www.w3.org/1999/html">Nyelv: Angol | </span> <span class="identifiers"> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="10.1007/s00222-018-00849-y" target="_blank" href="https://doi.org/10.1007/s00222-018-00849-y"> DOI </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="000469388500001" target="_blank" href="https://www.webofscience.com/wos/woscc/full-record/000469388500001"> WoS </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="85062704684" target="_blank" href="http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85062704684"> Scopus </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="http://link.springer.com/10.1007/s00222-018-00849-y" target="_blank" href="http://link.springer.com/10.1007/s00222-018-00849-y"> Egyéb URL </a> </span> </span> <OnlyViewableByAuthor><div class="ratings"> <div class="journal-subject">Folyóirat szakterülete: Scopus - Mathematics (miscellaneous)&nbsp;&nbsp;&nbsp;SJR indikátor:&nbsp;D1</div> </div></OnlyViewableByAuthor> <div class="publication-citation" style="margin-left: 0.5cm;"> <span title="Nyilvános idézőközlemények összesen, említések nélkül" class="citingPub-count">Nyilvános idéző összesen: 91</span> | Független: 74 | Függő: 17 | Nem jelölt: 0 | WoS jelölt: 85 | Scopus jelölt:&nbsp;62 | WoS/Scopus jelölt:&nbsp;87 | DOI jelölt:&nbsp;90 </div> <div class="publication-citation"> <a target="_blank" href="/api/publication?cond=citations.related;eq;30603311&sort=publishedYear,desc&sort=title"> Idézett közlemények száma: 10 </a> </div> <div class="mtid"><span class="long-pub-mtid">Közlemény: 30603311</span> | <span class="status-data status-VALIDATED"> Egyeztetett </span> Forrás Idéző | <span class="type-subtype">Folyóiratcikk ( Szakcikk ) </span> | <span class="pub-category">Tudományos</span> | <span class="publication-sourceOfData">kézi felvitel</span> </div> <div class="lastModified">Utolsó módosítás: 2020.12.23. 09:16 Szuper Admin (admin) </div> <pre class="comment" style="margin-top: 0; margin-bottom: 0;"><u>Megjegyzés</u>: MTA-BME Stochastics Research Group, Department of Stochastics, Budapest University of Technology and Economics, P.O. Box 91, Budapest, 1521, Hungary Einstein Institute of Mathematics, Edmond J. Safra Campus (Givat Ram), The Hebrew University, Jerusalem, 91904, Israel Export Date: 25 September 2019 Correspondence Address: Ho...</pre> </div></div>