Lodge, Russell; Lyubich, Mikhail; Merenkov, Sergei; Mukherjee, Sabyasachi On dynamical gaskets generated by rational maps, Kleinian groups, and Schwarz reflections. (English) Zbl 1517.37055 Conform. Geom. Dyn. 27, 1-54 (2023). Reviewer: Yongquan Zhang (Stony Brook) MSC: 37F32 37F31 37F10 37F20 30C62 30C10 30D05 30F40 30C45 28A78 PDFBibTeX XMLCite \textit{R. Lodge} et al., Conform. Geom. Dyn. 27, 1--54 (2023; Zbl 1517.37055) Full Text: DOI arXiv
Lyubich, Mikhail; Mukherjee, Sabyasachi Mirrors of conformal dynamics: Interplay between anti-rational maps, reflection groups, Schwarz reflections, and correspondences. arXiv:2310.03316 Preprint, arXiv:2310.03316 [math.DS] (2023). MSC: 37C85 37F05 37F10 37F31 37F32 37F34 37F46 30C10 30C20 30C62 30D05 30F35 BibTeX Cite \textit{M. Lyubich} and \textit{S. Mukherjee}, ``Mirrors of conformal dynamics: Interplay between anti-rational maps, reflection groups, Schwarz reflections, and correspondences'', Preprint, arXiv:2310.03316 [math.DS] (2023) Full Text: arXiv OA License
Lyubich, Mikhail; Mazor, Jacob; Mukherjee, Sabyasachi Antiholomorphic correspondences and mating I: realization theorems. arXiv:2303.02459 Preprint, arXiv:2303.02459 [math.DS] (2023). MSC: 37C85 37F05 37F10 37F31 37F32 37F34 37F46 30C10 30C20 30C62 30D05 30F35 BibTeX Cite \textit{M. Lyubich} et al., ``Antiholomorphic correspondences and mating I: realization theorems'', Preprint, arXiv:2303.02459 [math.DS] (2023) Full Text: arXiv OA License
Avila, Artur; Lyubich, Mikhail Lebesgue measure of Feigenbaum Julia sets. (English) Zbl 1494.37026 Ann. Math. (2) 195, No. 1, 1-88 (2022). Reviewer: Walter Bergweiler (Kiel) MSC: 37F10 37F25 37F20 37F35 30D05 PDFBibTeX XMLCite \textit{A. Avila} and \textit{M. Lyubich}, Ann. Math. (2) 195, No. 1, 1--88 (2022; Zbl 1494.37026) Full Text: DOI arXiv
Bleher, Pavel; Lyubich, Mikhail; Roeder, Roland Lee-Yang-Fisher zeros for the DHL and 2D rational dynamics. II: Global pluripotential interpretation. (English) Zbl 1437.82003 J. Geom. Anal. 30, No. 1, 777-833 (2020). MSC: 82B20 82B26 82B28 37F80 37F10 82D40 PDFBibTeX XMLCite \textit{P. Bleher} et al., J. Geom. Anal. 30, No. 1, 777--833 (2020; Zbl 1437.82003) Full Text: DOI arXiv
Lyubich, Mikhail; Merenkov, Sergei; Mukherjee, Sabyasachi; Ntalampekos, Dimitrios David extension of circle homeomorphisms, welding, mating, and removability. arXiv:2010.11256 Preprint, arXiv:2010.11256 [math.DS] (2020). MSC: 30C50 30C62 30C75 30D05 30J10 37F10 37F31 37F32 51F15 BibTeX Cite \textit{M. Lyubich} et al., ``David extension of circle homeomorphisms, welding, mating, and removability'', Preprint, arXiv:2010.11256 [math.DS] (2020) Full Text: arXiv OA License
Dang, Nguyen-Bac; Grigorchuk, Rostislav; Lyubich, Mikhail Self-similar groups and holomorphic dynamics: Renormalization, integrability, and spectrum. arXiv:2010.00675 Preprint, arXiv:2010.00675 [math.GR] (2020). MSC: 37A30 32H04 37F10 05C50 20E08 BibTeX Cite \textit{N.-B. Dang} et al., ``Self-similar groups and holomorphic dynamics: Renormalization, integrability, and spectrum'', Preprint, arXiv:2010.00675 [math.GR] (2020) Full Text: arXiv OA License
Lyubich, Mikhail; Merenkov, Sergei Quasisymmetries of the basilica and the Thompson group. (English) Zbl 1499.30238 Geom. Funct. Anal. 28, No. 3, 727-754 (2018). MSC: 30D05 20F65 37F10 37F44 PDFBibTeX XMLCite \textit{M. Lyubich} and \textit{S. Merenkov}, Geom. Funct. Anal. 28, No. 3, 727--754 (2018; Zbl 1499.30238) Full Text: DOI arXiv
Lee, Seung-Yeop; Lyubich, Mikhail; Makarov, Nikolai G.; Mukherjee, Sabyasachi Schwarz reflections and the Tricorn. arXiv:1812.01573 Preprint, arXiv:1812.01573 [math.DS] (2018). MSC: 37F10 37F20 37F31 37F32 37F46 30C45 30D05 30D40 82B21 BibTeX Cite \textit{S.-Y. Lee} et al., ``Schwarz reflections and the Tricorn'', Preprint, arXiv:1812.01573 [math.DS] (2018) Full Text: arXiv OA License
Lee, Seung-Yeop; Lyubich, Mikhail; Makarov, Nikolai G.; Mukherjee, Sabyasachi Dynamics of Schwarz reflections: the mating phenomena. arXiv:1811.04979 Preprint, arXiv:1811.04979 [math.DS] (2018). MSC: 37F10 37F30 30D05 30C45 76D27 82B21 BibTeX Cite \textit{S.-Y. Lee} et al., ``Dynamics of Schwarz reflections: the mating phenomena'', Preprint, arXiv:1811.04979 [math.DS] (2018) Full Text: arXiv OA License
Firsova, Tanya; Lyubich, Mikhail \(\lambda\)-lemma for families of Riemann surfaces and the critical loci of complex Hénon maps. (English) Zbl 1384.32013 Conform. Geom. Dyn. 21, 111-125 (2017). Reviewer: Xiao-Min Li (Qingdao) MSC: 32G15 32H50 37F10 37F30 PDFBibTeX XMLCite \textit{T. Firsova} and \textit{M. Lyubich}, Conform. Geom. Dyn. 21, 111--125 (2017; Zbl 1384.32013) Full Text: DOI arXiv
Bleher, Pavel; Lyubich, Mikhail; Roeder, Roland Lee-Yang zeros for the DHL and 2D rational dynamics. I: Foliation of the physical cylinder. (English. French summary) Zbl 1372.82011 J. Math. Pures Appl. (9) 107, No. 5, 491-590 (2017). Reviewer: Utkir A. Rozikov (Tashkent) MSC: 82B20 82B28 37D30 37F10 82B27 82D40 PDFBibTeX XMLCite \textit{P. Bleher} et al., J. Math. Pures Appl. (9) 107, No. 5, 491--590 (2017; Zbl 1372.82011) Full Text: DOI arXiv
Bonk, Mario; Lyubich, Mikhail; Merenkov, Sergei Quasisymmetries of Sierpiński carpet Julia sets. (English) Zbl 1358.37083 Adv. Math. 301, 383-422 (2016). Reviewer: Alexandr Yu. Rashkovsky (Stavanger) MSC: 37F10 30D05 37F50 PDFBibTeX XMLCite \textit{M. Bonk} et al., Adv. Math. 301, 383--422 (2016; Zbl 1358.37083) Full Text: DOI arXiv
Dujardin, Romain; Lyubich, Mikhail Stability and bifurcations for dissipative polynomial automorphisms of \(\mathbb C^2\). (English) Zbl 1337.37029 Invent. Math. 200, No. 2, 439-511 (2015). Reviewer: Feng Rong (Shanghai) MSC: 37F10 37G15 32H50 32M17 PDFBibTeX XMLCite \textit{R. Dujardin} and \textit{M. Lyubich}, Invent. Math. 200, No. 2, 439--511 (2015; Zbl 1337.37029) Full Text: DOI arXiv
Lyubich, Mikhail Analytic low-dimensional dynamics: from dimension one to two. (English) Zbl 1373.37103 Jang, Sun Young (ed.) et al., Proceedings of the International Congress of Mathematicians (ICM 2014), Seoul, Korea, August 13–21, 2014. Vol. I: Plenary lectures and ceremonies. Seoul: KM Kyung Moon Sa (ISBN 978-89-6105-804-9/hbk; 978-89-6105-803-2/set). 443-474 (2014). MSC: 37E05 37E20 37E30 37F10 37F25 37F30 37F45 PDFBibTeX XMLCite \textit{M. Lyubich}, in: Proceedings of the International Congress of Mathematicians (ICM 2014), Seoul, Korea, August 13--21, 2014. Vol. I: Plenary lectures and ceremonies. Seoul: KM Kyung Moon Sa. 443--474 (2014; Zbl 1373.37103)
Benini, Anna Miriam; Lyubich, Mikhail Repelling periodic points and landing of rays for post-singularly bounded exponential maps. (Points périodiques répulsifs et atterrissage de rayons pour les fonctions exponentielles avec orbite singulière limitée.) (English. French summary) Zbl 1323.37029 Ann. Inst. Fourier 64, No. 4, 1493-1520 (2014). Reviewer: Alexandre De Zotti (Liverpool) MSC: 37F10 37F20 37F45 PDFBibTeX XMLCite \textit{A. M. Benini} and \textit{M. Lyubich}, Ann. Inst. Fourier 64, No. 4, 1493--1520 (2014; Zbl 1323.37029) Full Text: DOI arXiv Link
Bonifant, Araceli (ed.); Lyubich, Mikhail (ed.); Sutherland, Scott (ed.) Frontiers in complex dynamics. In celebration of John Milnor’s 80th birthday. Based on a conference, Banff, Canada, February 2011. (English) Zbl 1285.37001 Princeton Mathematical Series 51. Princeton, NJ: Princeton University Press (ISBN 978-0-691-15929-4/hbk; 978-1-400-85131-7/ebook). xii, 787 p. (2014). MSC: 37-06 37F10 37F45 37F50 32A10 32A20 32H02 32H04 37B40 20E07 53C12 53C55 00B25 00B30 PDFBibTeX XMLCite \textit{A. Bonifant} (ed.) et al., Frontiers in complex dynamics. In celebration of John Milnor's 80th birthday. Based on a conference, Banff, Canada, February 2011. Princeton, NJ: Princeton University Press (2014; Zbl 1285.37001)
Lyubich, Mikhail Forty years of unimodal dynamics: on the occasion of Artur Avila winning the Brin Prize. (English) Zbl 1280.37036 J. Mod. Dyn. 6, No. 2, 183-203 (2012). Reviewer: Alexey A. Glutsyuk (Lyon) MSC: 37E05 37E20 37F10 37F35 37F45 37F50 37D20 37D25 37D45 37C40 37C45 37-02 PDFBibTeX XMLCite \textit{M. Lyubich}, J. Mod. Dyn. 6, No. 2, 183--203 (2012; Zbl 1280.37036) Full Text: DOI
Avila, Artur; Lyubich, Mikhail; Shen, Weixiao Parapuzzle of the Multibrot set and typical dynamics of unimodal maps. (English) Zbl 1213.37076 J. Eur. Math. Soc. (JEMS) 13, No. 1, 27-56 (2011). Reviewer: Yuefei Wang (Beijing) MSC: 37F45 37F10 PDFBibTeX XMLCite \textit{A. Avila} et al., J. Eur. Math. Soc. (JEMS) 13, No. 1, 27--56 (2011; Zbl 1213.37076) Full Text: DOI arXiv
Avila, Artur; Kahn, Jeremy; Lyubich, Mikhail; Shen, Weixiao Combinatorial rigidity for unicritical polynomials. (English) Zbl 1204.37047 Ann. Math. (2) 170, No. 2, 783-797 (2009). Reviewer: Rainer Brück (Dortmund) MSC: 37F45 PDFBibTeX XMLCite \textit{A. Avila} et al., Ann. Math. (2) 170, No. 2, 783--797 (2009; Zbl 1204.37047) Full Text: DOI arXiv Link
Kahn, Jeremy; Lyubich, Mikhail Local connectivity of Julia sets for unicritical polynomials. (English) Zbl 1180.37072 Ann. Math. (2) 170, No. 1, 413-426 (2009). Reviewer: Walter Bergweiler (Kiel) MSC: 37F50 37F10 30D05 PDFBibTeX XMLCite \textit{J. Kahn} and \textit{M. Lyubich}, Ann. Math. (2) 170, No. 1, 413--426 (2009; Zbl 1180.37072) Full Text: DOI arXiv Link
Petersen, Carsten Lunde (ed.); Lyubich, Mikhail (ed.); Schleicher, Dierk (ed.); Smillie, John (ed.) Trends and developments in complex dynamics. Abstracts from the workshop held October 19th – October 25th, 2008. (English) Zbl 1177.37010 Oberwolfach Rep. 5, No. 4, 2703-2762 (2008). MSC: 37-06 37F15 37F45 37F10 37F30 00B05 PDFBibTeX XMLCite \textit{C. L. Petersen} (ed.) et al., Oberwolfach Rep. 5, No. 4, 2703--2762 (2008; Zbl 1177.37010) Full Text: DOI Link
Kahn, Jeremy; Lyubich, Mikhail A priori bounds for some infinitely renormalizable quadratics. II: Decorations. (English) Zbl 1156.37311 Ann. Sci. Éc. Norm. Supér. (4) 41, No. 1, 57-84 (2008). MSC: 37F10 PDFBibTeX XMLCite \textit{J. Kahn} and \textit{M. Lyubich}, Ann. Sci. Éc. Norm. Supér. (4) 41, No. 1, 57--84 (2008; Zbl 1156.37311) Full Text: DOI arXiv Link
Avila, Artur; Lyubich, Mikhail Hausdorff dimension and conformal measures of Feigenbaum Julia sets. (English) Zbl 1205.37058 J. Am. Math. Soc. 21, No. 2, 305-363 (2008). MSC: 37F35 37F25 37F10 PDFBibTeX XMLCite \textit{A. Avila} and \textit{M. Lyubich}, J. Am. Math. Soc. 21, No. 2, 305--363 (2008; Zbl 1205.37058) Full Text: DOI arXiv
De Carvalho, A.; Lyubich, M.; Martens, M. Renormalization in the Hénon family. I: Universality but non-rigidity. (English) Zbl 1098.37039 J. Stat. Phys. 121, No. 5-6, 611-669 (2005). Reviewer: Alois Klíč (Praha) MSC: 37E20 37F10 37D35 37D45 37E05 37E30 PDFBibTeX XMLCite \textit{A. De Carvalho} et al., J. Stat. Phys. 121, No. 5--6, 611--669 (2005; Zbl 1098.37039) Full Text: DOI arXiv
Kaimanovich, Vadim A.; Lyubich, Mikhail Conformal and harmonic measures on laminations associated with rational maps. (English) Zbl 1242.37032 Mem. Am. Math. Soc. 820, 119 p. (2005). MSC: 37F35 30F40 30F45 37F10 37F30 30D05 57M50 28A12 57R30 53C12 37-02 PDFBibTeX XMLCite \textit{V. A. Kaimanovich} and \textit{M. Lyubich}, Conformal and harmonic measures on laminations associated with rational maps. Providence, RI: American Mathematical Society (AMS) (2005; Zbl 1242.37032) Full Text: DOI Link
Lyubich, Mikhail Dynamics of quadratic polynomials. III: Parapuzzle and SRB measures. (English) Zbl 1044.37038 Flexor, Marguerite (ed.) et al., Complex geometry and dynamical systems. Conference in honor of Adrien Douady on the occasion of his 60th birthday, Orsay, France, July 3–8, 1995. Paris: Astérisque. Astérisque 261, 173-200 (2000). MSC: 37F10 37F15 37F25 PDFBibTeX XMLCite \textit{M. Lyubich}, Astérisque 261, 173--200 (2000; Zbl 1044.37038) Full Text: arXiv
Lyubich, Mikhail Dynamics of quadratic polynomials. I, II. (English) Zbl 0908.58053 Acta Math. 178, No. 2, 185-297 (1997). Reviewer: G.Swiatek (University Park) MSC: 37F99 37E99 30D10 PDFBibTeX XMLCite \textit{M. Lyubich}, Acta Math. 178, No. 2, 185--297 (1997; Zbl 0908.58053) Full Text: DOI
Lyubich, Mikhail; Yampolsky, Michael Dynamics of quadratic polynomials: complex bounds for real maps. (English) Zbl 0881.58053 Ann. Inst. Fourier 47, No. 4, 1219-1255 (1997). MSC: 37F99 30D05 37E99 PDFBibTeX XMLCite \textit{M. Lyubich} and \textit{M. Yampolsky}, Ann. Inst. Fourier 47, No. 4, 1219--1255 (1997; Zbl 0881.58053) Full Text: DOI arXiv Numdam EuDML
Lyubich, Mikhail Renormalization ideas in conformal dynamics. (English) Zbl 0877.58046 Bott, Raoul (ed.) et al., Current developments in mathematics, 1995. Lectures of a seminar, held in Boston, MA, USA, May 7-8, 1995. Cambridge, MA: International Press. 109-133 (155-190 preliminary version 1994) (1995). Reviewer: G.Świątek (University Park) MSC: 37F99 37E99 30F60 30C10 PDFBibTeX XMLCite \textit{M. Lyubich}, in: Current developments in mathematics, 1995. Lectures of a seminar, held in Boston, MA, USA, May 7-8, 1995. Cambridge, MA: International Press. 109--133 (155--190, preliminary version 1994) (1995; Zbl 0877.58046)
Bedford, Eric; Lyubich, Mikhail; Smillie, John Polynomial diffeomorphisms of \(\mathbb{C}^ 2\). IV: The measure of maximal entropy and laminar currents. (English) Zbl 0792.58034 Invent. Math. 112, No. 1, 77-125 (1993). Reviewer: I.Mihai (Bucureşti) MSC: 37F10 32H50 58C35 58A25 PDFBibTeX XMLCite \textit{E. Bedford} et al., Invent. Math. 112, No. 1, 77--125 (1993; Zbl 0792.58034) Full Text: DOI arXiv EuDML