Hochman, Michael Irreducibility and periodicity in \(\mathbb{Z}^{2}\) symbolic systems. arXiv:2401.02273 Preprint, arXiv:2401.02273 [math.DS] (2024). MSC: 37B05 37B10 37B51 BibTeX Cite \textit{M. Hochman}, ``Irreducibility and periodicity in $\mathbb{Z}^{2}$ symbolic systems'', Preprint, arXiv:2401.02273 [math.DS] (2024) Full Text: arXiv OA License
Hochman, Michael Some remarks about self-products and entropy. arXiv:2312.15812 Preprint, arXiv:2312.15812 [math.DS] (2023). MSC: 37B40 37B20 37A35 BibTeX Cite \textit{M. Hochman}, ``Some remarks about self-products and entropy'', Preprint, arXiv:2312.15812 [math.DS] (2023) Full Text: arXiv OA License
Hochman, Michael On the analytic self-maps of Cantor sets in the line. arXiv:2312.15810 Preprint, arXiv:2312.15810 [math.DS] (2023). MSC: 26A30 37E05 BibTeX Cite \textit{M. Hochman}, ``On the analytic self-maps of Cantor sets in the line'', Preprint, arXiv:2312.15810 [math.DS] (2023) Full Text: arXiv OA License
Hochman, Michael A short proof of Host’s equidistribution theorem. (English) Zbl 1514.37014 Isr. J. Math. 251, No. 2, 527-539 (2022). MSC: 37A30 37A20 PDFBibTeX XMLCite \textit{M. Hochman}, Isr. J. Math. 251, No. 2, 527--539 (2022; Zbl 1514.37014) Full Text: DOI arXiv
Hochman, Michael; Rapaport, Ariel Hausdorff dimension of planar self-affine sets and measures with overlaps. (English) Zbl 1502.28005 J. Eur. Math. Soc. (JEMS) 24, No. 7, 2361-2441 (2022). Reviewer: Haipeng Chen (Shenzhen) MSC: 28A80 28A78 37C45 PDFBibTeX XMLCite \textit{M. Hochman} and \textit{A. Rapaport}, J. Eur. Math. Soc. (JEMS) 24, No. 7, 2361--2441 (2022; Zbl 1502.28005) Full Text: DOI arXiv
Bárány, Balázs; Hochman, Michael; Rapaport, Ariel Hausdorff dimension of planar self-affine sets and measures. (English) Zbl 1414.28014 Invent. Math. 216, No. 3, 601-659 (2019). Reviewer: George Stoica (Saint John) MSC: 28A80 37C45 37F35 PDFBibTeX XMLCite \textit{B. Bárány} et al., Invent. Math. 216, No. 3, 601--659 (2019; Zbl 1414.28014) Full Text: DOI arXiv
Algom, Amir; Hochman, Michael Self-embeddings of Bedford-McMullen carpets. (English) Zbl 1411.28005 Ergodic Theory Dyn. Syst. 39, No. 3, 577-603 (2019). MSC: 28A80 PDFBibTeX XMLCite \textit{A. Algom} and \textit{M. Hochman}, Ergodic Theory Dyn. Syst. 39, No. 3, 577--603 (2019; Zbl 1411.28005) Full Text: DOI arXiv
Hochman, Michael Every Borel automorphism without finite invariant measures admits a two-set generator. (English) Zbl 1415.37016 J. Eur. Math. Soc. (JEMS) 21, No. 1, 271-317 (2019). Reviewer: Marcin Kulczycki (Kraków) MSC: 37B10 37A35 37A40 37A99 PDFBibTeX XMLCite \textit{M. Hochman}, J. Eur. Math. Soc. (JEMS) 21, No. 1, 271--317 (2019; Zbl 1415.37016) Full Text: DOI arXiv
Hochman, Michael Dimension theory of self-similar sets and measures. (English) Zbl 1447.28007 Sirakov, Boyan (ed.) et al., Proceedings of the international congress of mathematicians 2018, ICM 2018, Rio de Janeiro, Brazil, August 1–9, 2018. Volume III. Invited lectures. Hackensack, NJ: World Scientific; Rio de Janeiro: Sociedade Brasileira de Matemática (SBM). 1949-1972 (2018). MSC: 28A80 37C45 37F35 PDFBibTeX XMLCite \textit{M. Hochman}, in: Proceedings of the international congress of mathematicians 2018, ICM 2018, Rio de Janeiro, Brazil, August 1--9, 2018. Volume III. Invited lectures. Hackensack, NJ: World Scientific; Rio de Janeiro: Sociedade Brasileira de Matemática (SBM). 1949--1972 (2018; Zbl 1447.28007) Full Text: DOI
Hochman, Michael Smooth symmetries of \(\times a\)-invariant sets. (English) Zbl 1406.28004 J. Mod. Dyn. 13, 187-197 (2018). MSC: 28A80 11K55 PDFBibTeX XMLCite \textit{M. Hochman}, J. Mod. Dyn. 13, 187--197 (2018; Zbl 1406.28004) Full Text: DOI arXiv
Breuillard, Emmanuel (ed.); Hochman, Michael (ed.); Shmerkin, Pablo (ed.) Working session: Additive combinatorics, entropy, and fractal geometry. Abstracts from the working session held October 8–13, 2017. (Arbeitsgemeinschaft: Additive combinatorics, entropy, and fractal geometry.) (English) Zbl 1409.00074 Oberwolfach Rep. 14, No. 4, 2847-2905 (2017). MSC: 00B05 00B25 28A80 28A75 37A25 28-06 11-06 PDFBibTeX XMLCite \textit{E. Breuillard} (ed.) et al., Oberwolfach Rep. 14, No. 4, 2847--2905 (2017; Zbl 1409.00074) Full Text: DOI
Hochman, Michael Some problems on the boundary of fractal geometry and additive combinatorics. (English) Zbl 1383.28002 Barral, Julien (ed.) et al., Recent developments in fractals and related fields. Conference on fractals and related fields III, Ile de Porquerolles, France, September 2015. Cham: Birkhäuser/Springer (ISBN 978-3-319-57803-3/hbk; 978-3-319-57805-7/ebook). Trends in Mathematics, 129-174 (2017). MSC: 28A80 28A78 PDFBibTeX XMLCite \textit{M. Hochman}, in: Recent developments in fractals and related fields. Conference on fractals and related fields III, Ile de Porquerolles, France, September 2015. Cham: Birkhäuser/Springer. 129--174 (2017; Zbl 1383.28002) Full Text: DOI arXiv
Hochman, Michael; Solomyak, Boris On the dimension of Furstenberg measure for \({SL}_{2}(\mathbb {R})\) random matrix products. (English) Zbl 1398.37012 Invent. Math. 210, No. 3, 815-875 (2017). Reviewer: Phillip Wesolek (Binghamton) MSC: 37A45 37A35 22D40 PDFBibTeX XMLCite \textit{M. Hochman} and \textit{B. Solomyak}, Invent. Math. 210, No. 3, 815--875 (2017; Zbl 1398.37012) Full Text: DOI arXiv
Hochman, Michael; Vanier, Pascal Turing degree spectra of minimal subshifts. (English) Zbl 1491.03031 Weil, Pascal (ed.), Computer science – theory and applications. 12th international computer science symposium in Russia, CSR 2017, Kazan, Russia, June 8–12, 2017. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 10304, 154-161 (2017). MSC: 03D30 37B10 PDFBibTeX XMLCite \textit{M. Hochman} and \textit{P. Vanier}, Lect. Notes Comput. Sci. 10304, 154--161 (2017; Zbl 1491.03031) Full Text: DOI arXiv
Hochman, Michael Multidimensional shifts of finite type and sofic shifts. (English) Zbl 1377.37030 Berthé, Valérie (ed.) et al., Combinatorics, words and symbolic dynamics. Cambridge: Cambridge University Press (ISBN 978-1-107-07702-7/hbk; 978-1-139-92473-3/ebook). Encyclopedia of Mathematics and its Applications 159, 296-358 (2016). Reviewer: Thomas B. Ward (Leeds) MSC: 37B50 37B10 PDFBibTeX XMLCite \textit{M. Hochman}, Encycl. Math. Appl. 159, 296--358, bibliography 443--463 (2016; Zbl 1377.37030) Full Text: DOI DOI
Hochman, Michael; Shmerkin, Pablo Equidistribution from fractal measures. (English) Zbl 1409.11054 Invent. Math. 202, No. 1, 427-479 (2015). MSC: 11K16 11A63 28A80 28D05 PDFBibTeX XMLCite \textit{M. Hochman} and \textit{P. Shmerkin}, Invent. Math. 202, No. 1, 427--479 (2015; Zbl 1409.11054) Full Text: DOI arXiv
Hochman, Michael On self-similar sets with overlaps and inverse theorems for entropy in \(\mathbb{R}^d\). arXiv:1503.09043 Preprint, arXiv:1503.09043 [math.CA] (2015). MSC: 28A80 11K55 11B30 11P70 BibTeX Cite \textit{M. Hochman}, ``On self-similar sets with overlaps and inverse theorems for entropy in $\mathbb{R}^d$'', Preprint, arXiv:1503.09043 [math.CA] (2015) Full Text: arXiv OA License
Hochman, Michael Self similar sets, entropy and additive combinatorics. (English) Zbl 1318.28025 Feng, De-Jun (ed.) et al., Geometry and analysis of fractals. Based on the international conference on advances of fractals and related topics, Hong Kong, China, December 10–14, 2012. Berlin: Springer (ISBN 978-3-662-43919-7/hbk; 978-3-662-43920-3/ebook). Springer Proceedings in Mathematics & Statistics 88, 225-252 (2014). MSC: 28A80 PDFBibTeX XMLCite \textit{M. Hochman}, Springer Proc. Math. Stat. 88, 225--252 (2014; Zbl 1318.28025) Full Text: DOI arXiv
Hochman, Michael Lectures on dynamics, fractal geometry, and metric number theory. (English) Zbl 1314.28008 J. Mod. Dyn. 8, No. 3-4, 437-497 (2014). MSC: 28A80 37F99 37A99 PDFBibTeX XMLCite \textit{M. Hochman}, J. Mod. Dyn. 8, No. 3--4, 437--497 (2014; Zbl 1314.28008) Full Text: DOI
Hochman, Michael On self-similar sets with overlaps and inverse theorems for entropy. (English) Zbl 1337.28015 Ann. Math. (2) 180, No. 2, 773-822 (2014). Reviewer: Peter Massopust (München) MSC: 28A80 37L40 37C35 28D20 PDFBibTeX XMLCite \textit{M. Hochman}, Ann. Math. (2) 180, No. 2, 773--822 (2014; Zbl 1337.28015) Full Text: DOI arXiv
Hochman, Michael Erratum to: “Geometric rigidity of \(\times m\) invariant measures”. (English) Zbl 1328.37002 J. Eur. Math. Soc. (JEMS) 15, No. 6, 2463-2464 (2013). MSC: 37A10 37E10 37A45 37C45 28A80 PDFBibTeX XMLCite \textit{M. Hochman}, J. Eur. Math. Soc. (JEMS) 15, No. 6, 2463--2464 (2013; Zbl 1328.37002) Full Text: DOI
Hochman, Michael Erratum to: Isomorphism and embedding of Borel systems on full sets. (English) Zbl 1281.37007 Acta Appl. Math. 128, No. 1, 211 (2013). MSC: 37A35 37A05 PDFBibTeX XMLCite \textit{M. Hochman}, Acta Appl. Math. 128, No. 1, 211 (2013; Zbl 1281.37007) Full Text: DOI arXiv
Hochman, Michael On the ratio ergodic theorem for group actions. (English) Zbl 1310.37005 J. Lond. Math. Soc., II. Ser. 88, No. 2, 465-482 (2013). Reviewer: Tim Austin (New York) MSC: 37A30 37A40 28D15 47A35 PDFBibTeX XMLCite \textit{M. Hochman}, J. Lond. Math. Soc., II. Ser. 88, No. 2, 465--482 (2013; Zbl 1310.37005) Full Text: DOI arXiv
Hochman, Michael Isomorphism and embedding of Borel systems on full sets. (English) Zbl 1339.37007 Acta Appl. Math. 126, No. 1, 187-201 (2013); erratum ibid. 128, No. 1, 128 (2013). Reviewer: Tim Austin (New York) MSC: 37A35 37A05 37C40 PDFBibTeX XMLCite \textit{M. Hochman}, Acta Appl. Math. 126, No. 1, 187--201 (2013; Zbl 1339.37007) Full Text: DOI
Damron, Michael; Hochman, Michael Examples of nonpolygonal limit shapes in i.i.d. first-passage percolation and infinite coexistence in spatial growth models. (English) Zbl 1314.60154 Ann. Appl. Probab. 23, No. 3, 1074-1085 (2013). MSC: 60K35 82B43 PDFBibTeX XMLCite \textit{M. Damron} and \textit{M. Hochman}, Ann. Appl. Probab. 23, No. 3, 1074--1085 (2013; Zbl 1314.60154) Full Text: DOI arXiv Euclid
Chazottes, J.-R.; Gambaudo, J.-M.; Hochman, M.; Ugalde, E. On the finite-dimensional marginals of shift-invariant measures. (English) Zbl 1263.37027 Ergodic Theory Dyn. Syst. 32, No. 5, 1485-1500 (2012). MSC: 37B50 37B10 37A25 PDFBibTeX XMLCite \textit{J. R. Chazottes} et al., Ergodic Theory Dyn. Syst. 32, No. 5, 1485--1500 (2012; Zbl 1263.37027) Full Text: DOI arXiv
Hochman, Michael Geometric rigidity of \(\times m\) invariant measures. (English) Zbl 1253.37007 J. Eur. Math. Soc. (JEMS) 14, No. 5, 1539-1563 (2012); erratum ibid. 15, No. 6, 2463-2464 (2013). Reviewer: Thomas B. Ward (Durham) MSC: 37A10 37E10 37A45 37C45 28A80 PDFBibTeX XMLCite \textit{M. Hochman}, J. Eur. Math. Soc. (JEMS) 14, No. 5, 1539--1563 (2012; Zbl 1253.37007) Full Text: DOI arXiv
Hochman, Michael; Siemanszko, Artur Inverses, powers and Cartesian products of topologically deterministic maps. (English) Zbl 1271.37024 Topol. Methods Nonlinear Anal. 39, No. 1, 189-198 (2012). MSC: 37B40 54H20 PDFBibTeX XMLCite \textit{M. Hochman} and \textit{A. Siemanszko}, Topol. Methods Nonlinear Anal. 39, No. 1, 189--198 (2012; Zbl 1271.37024) Full Text: arXiv
Hochman, Michael Slow entropy and differentiable models for infinite-measure preserving \(\mathbb z^{k}\) actions. (English) Zbl 1273.37022 Ergodic Theory Dyn. Syst. 32, No. 2, 653-674 (2012). Reviewer: Thomas B. Ward (Durham) MSC: 37C85 37A35 37A30 PDFBibTeX XMLCite \textit{M. Hochman}, Ergodic Theory Dyn. Syst. 32, No. 2, 653--674 (2012; Zbl 1273.37022) Full Text: DOI arXiv
Hochman, Michael; Shmerkin, Pablo Local entropy averages and projections of fractal measures. (English) Zbl 1251.28008 Ann. Math. (2) 175, No. 3, 1001-1059 (2012). Reviewer: Takahisa Miyata (Kobe) MSC: 28A80 28A78 PDFBibTeX XMLCite \textit{M. Hochman} and \textit{P. Shmerkin}, Ann. Math. (2) 175, No. 3, 1001--1059 (2012; Zbl 1251.28008) Full Text: DOI arXiv
Hochman, Michael On notions of determinism in topological dynamics. (English) Zbl 1244.37012 Ergodic Theory Dyn. Syst. 32, No. 1, 119-140 (2012). Reviewer: Piotr Oprocha (Kraków) MSC: 37B40 37B10 37A25 PDFBibTeX XMLCite \textit{M. Hochman}, Ergodic Theory Dyn. Syst. 32, No. 1, 119--140 (2012; Zbl 1244.37012) Full Text: DOI arXiv
Hochman, Michael Rohlin properties for \(\mathbb {Z}^{d}\) actions on the Cantor set. (English) Zbl 1273.37020 Trans. Am. Math. Soc. 364, No. 3, 1127-1143 (2012). Reviewer: Thomas B. Ward (Durham) MSC: 37C50 37C85 37B50 54H20 03D99 PDFBibTeX XMLCite \textit{M. Hochman}, Trans. Am. Math. Soc. 364, No. 3, 1127--1143 (2012; Zbl 1273.37020) Full Text: DOI arXiv
Hochman, Michael Non-expansive directions for \(\mathbb Z^{2}\) actions. (English) Zbl 1211.37013 Ergodic Theory Dyn. Syst. 31, No. 1, 91-112 (2011). Reviewer: Vladimir Răsvan (Craiova) MSC: 37B15 37B05 68Q80 PDFBibTeX XMLCite \textit{M. Hochman}, Ergodic Theory Dyn. Syst. 31, No. 1, 91--112 (2011; Zbl 1211.37013) Full Text: DOI arXiv
Chazottes, Jean-René; Hochman, Michael On the zero-temperature limit of Gibbs states. (English) Zbl 1203.82015 Commun. Math. Phys. 297, No. 1, 265-281 (2010). Reviewer: Iván Abonyi (Budapest) MSC: 82B20 82B05 PDFBibTeX XMLCite \textit{J.-R. Chazottes} and \textit{M. Hochman}, Commun. Math. Phys. 297, No. 1, 265--281 (2010; Zbl 1203.82015) Full Text: DOI arXiv
Hochman, Michael On the automorphism groups of multidimensional shifts of finite type. (English) Zbl 1202.37018 Ergodic Theory Dyn. Syst. 30, No. 3, 809-840 (2010). Reviewer: Mohammad Reza Molaei (Kerman) MSC: 37B40 PDFBibTeX XMLCite \textit{M. Hochman}, Ergodic Theory Dyn. Syst. 30, No. 3, 809--840 (2010; Zbl 1202.37018) Full Text: DOI
Hochman, Michael; Meyerovitch, Tom A characterization of the entropies of multidimensional shifts of finite type. (English) Zbl 1192.37022 Ann. Math. (2) 171, No. 3, 2011-2038 (2010). Reviewer: Vladimir Răsvan (Craiova) MSC: 37B50 37B10 37B40 37M25 94A17 PDFBibTeX XMLCite \textit{M. Hochman} and \textit{T. Meyerovitch}, Ann. Math. (2) 171, No. 3, 2011--2038 (2010; Zbl 1192.37022) Full Text: DOI arXiv Link
Hochman, Michael A ratio ergodic theorem for multiparameter non-singular actions. (English) Zbl 1190.22007 J. Eur. Math. Soc. (JEMS) 12, No. 2, 365-383 (2010). Reviewer: Victor Sharapov (Volgograd) MSC: 22D40 37A15 37A30 37A40 47A35 PDFBibTeX XMLCite \textit{M. Hochman}, J. Eur. Math. Soc. (JEMS) 12, No. 2, 365--383 (2010; Zbl 1190.22007) Full Text: DOI arXiv Link
Hochman, Michael Dynamics on fractals and fractal distributions. arXiv:1008.3731 Preprint, arXiv:1008.3731 [math.DS] (2010). MSC: 37C45 37A10 28A80 28A33 BibTeX Cite \textit{M. Hochman}, ``Dynamics on fractals and fractal distributions'', Preprint, arXiv:1008.3731 [math.DS] (2010) Full Text: arXiv OA License
Hochman, Michael Upcrossing inequalities for stationary sequences and applications. (English) Zbl 1196.37014 Ann. Probab. 37, No. 6, 2135-2149 (2009). Reviewer: Michael L. Blank (Moskva) MSC: 37A30 37A35 60G10 60G17 94A17 68Q30 PDFBibTeX XMLCite \textit{M. Hochman}, Ann. Probab. 37, No. 6, 2135--2149 (2009; Zbl 1196.37014) Full Text: DOI arXiv
Hochman, Michael A note on universality in multidimensional symbolic dynamics. (English) Zbl 1175.37019 Discrete Contin. Dyn. Syst., Ser. S 2, No. 2, 301-314 (2009). MSC: 37B15 37B40 37B50 94A17 03D45 PDFBibTeX XMLCite \textit{M. Hochman}, Discrete Contin. Dyn. Syst., Ser. S 2, No. 2, 301--314 (2009; Zbl 1175.37019) Full Text: DOI arXiv
Hochman, Michael On the dynamics and recursive properties of multidimensional symbolic systems. (English) Zbl 1168.37002 Invent. Math. 176, No. 1, 131-167 (2009). Reviewer: Vladimir Răsvan (Craiova) MSC: 37B50 37B15 37B40 68Q80 PDFBibTeX XMLCite \textit{M. Hochman}, Invent. Math. 176, No. 1, 131--167 (2009; Zbl 1168.37002) Full Text: DOI Backlinks: MO
Gutman, Yonatan; Hochman, Michael On processes which cannot be distinguished by finite observation. (English) Zbl 1149.37005 Isr. J. Math. 164, 265-284 (2008). Reviewer: Alexander Kachurovskij (Novosibirsk) MSC: 37A35 37A50 60G10 PDFBibTeX XMLCite \textit{Y. Gutman} and \textit{M. Hochman}, Isr. J. Math. 164, 265--284 (2008; Zbl 1149.37005) Full Text: DOI arXiv
Hochman, Michael Genericity in topological dynamics. (English) Zbl 1171.37305 Ergodic Theory Dyn. Syst. 28, No. 1, 125-165 (2008). MSC: 37B10 37C20 54H20 37B05 37A05 PDFBibTeX XMLCite \textit{M. Hochman}, Ergodic Theory Dyn. Syst. 28, No. 1, 125--165 (2008; Zbl 1171.37305) Full Text: DOI arXiv
Hochman, Michael Averaging sequences and abelian rank in amenable groups. (English) Zbl 1180.43001 Isr. J. Math. 158, 119-128 (2007). Reviewer: Tianxuan Miao (Thunder Bay) MSC: 43A07 PDFBibTeX XMLCite \textit{M. Hochman}, Isr. J. Math. 158, 119--128 (2007; Zbl 1180.43001) Full Text: DOI arXiv
Hochman, Michael Return times, recurrence densities and entropy for actions of some discrete amenable groups. (English) Zbl 1173.37303 J. Anal. Math. 100, 1-51 (2006). MSC: 37A35 28D15 28D20 PDFBibTeX XMLCite \textit{M. Hochman}, J. Anal. Math. 100, 1--51 (2006; Zbl 1173.37303) Full Text: DOI arXiv