## Lyubich, Mikhail

Compute Distance To:
 Author ID: lyubich.mikhail Published as: Lyubich, Mikhail; Lyubich, M. Yu.; Lyubich, M.; Lyubich, Mikhail Yur’evich more...less Further Spellings: Любич Михаил Юрьевич Homepage: http://www.math.stonybrook.edu/~mlyubich/ External Links: MGP · Wikidata · Math-Net.Ru · GND · IdRef
 Documents Indexed: 104 Publications since 1979, including 1 Book 8 Contributions as Editor Biographic References: 1 Publication Co-Authors: 55 Co-Authors with 77 Joint Publications 1,617 Co-Co-Authors
all top 5

### Co-Authors

 35 single-authored 12 Blokh, Alexander M. 7 Avila, Artur 7 Lyubich, Yuriĭ Il’ich 6 Eremenko, Alexandre Émmanuilovich 6 Kahn, Jeremy Adam 5 Martens, Marco 3 Bleher, Pavel M. 3 Smillie, John 2 Bedford, Eric 2 Firsova, Tanya 2 Merenkov, Sergei 2 Milnor, John Willard 2 Minsky, Yair N. 2 Peters, Han 2 Radu, Remus 2 Roeder, Roland K. W. 2 Shen, Weixiao 2 Suvorov, V. V. 2 Tanase, Raluca 2 Volberg, Alexander Lvovich 2 Yampolsky, Michael 1 Azarin, Vladimir S. 1 Benini, Anna Miriam 1 Bonifant, Araceli M. 1 Bonk, Mario 1 de Melo, Welington 1 Dudko, Dzmitry 1 Dujardin, Romain 1 Eells, James jun. 1 Forni, Giovanni 1 Ghys, Étienne 1 Giner, V. B. 1 Hazard, P. E. 1 Ji, Lizhen 1 Kaimanovich, Vadim A. 1 Khanin, Konstantin M. 1 Lee, Seung-Yeop 1 Lyubich, Lilya 1 Makarov, Nikolai Georgievich 1 McMullen, Curtis Tracy 1 Mukherjee, Sabyasachi 1 Palis, Jacob jun. 1 Petersen, Carsten Lunde 1 Pugh, Charles Chapman 1 Rempe-Gillen, Lasse 1 Salles de Carvalho, André 1 Schleicher, Dierk 1 Seade, Jose Antonio 1 Selinger, Nikita 1 Shub, Michael 1 Siggia, Eric D. 1 Sinaĭ, Yakov Grigor’evich 1 Sutherland, Scott 1 Takhtajan, Leon Armenovich 1 Yau, Shing-Tung
all top 5

### Serials

 7 Annals of Mathematics. Second Series 5 Inventiones Mathematicae 5 Journal of Soviet Mathematics 5 Soviet Mathematics. Doklady 5 Teoriya Funktsiĭ, Funktsional’nyĭ Analiz i ikh Prilozheniya 4 Functional Analysis and its Applications 3 Communications in Mathematical Physics 3 Russian Mathematical Surveys 3 Annales de l’Institut Fourier 3 Ergodic Theory and Dynamical Systems 3 Journal of the American Mathematical Society 2 Ukrainian Mathematical Journal 2 Advances in Mathematics 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Selecta Mathematica Sovietica 2 Leningrad Mathematical Journal 2 Geometric and Functional Analysis. GAFA 2 Notices of the American Mathematical Society 2 Journal of the European Mathematical Society (JEMS) 2 Contemporary Mathematics 2 Fields Institute Communications 1 Journal of Statistical Physics 1 Mathematical Notes 1 Nonlinearity 1 Uspekhi Matematicheskikh Nauk [N. S.] 1 Acta Mathematica 1 Funktsional’nyĭ Analiz i ego Prilozheniya 1 Gazette des Mathématiciens 1 Publications Mathématiques 1 Journal of Differential Geometry 1 Journal of the London Mathematical Society. Second Series 1 Memoirs of the American Mathematical Society 1 Publicationes Mathematicae Debrecen 1 Siberian Mathematical Journal 1 Algebra i Analiz 1 The Journal of Geometric Analysis 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the National Academy of Sciences of the United States of America 1 Journal of Knot Theory and its Ramifications 1 Journal of Difference Equations and Applications 1 The Journal of Fourier Analysis and Applications 1 Conformal Geometry and Dynamics 1 Oberwolfach Reports 1 Pure and Applied Mathematics Quarterly 1 Princeton Mathematical Series 1 Proceedings of Symposia in Pure Mathematics 1 Journal of Modern Dynamics 1 Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta Imeni V. A. Steklova
all top 5

### Fields

 94 Dynamical systems and ergodic theory (37-XX) 32 Functions of a complex variable (30-XX) 10 Measure and integration (28-XX) 9 Several complex variables and analytic spaces (32-XX) 8 General and overarching topics; collections (00-XX) 7 Group theory and generalizations (20-XX) 7 Differential geometry (53-XX) 5 Topological groups, Lie groups (22-XX) 4 History and biography (01-XX) 4 Operator theory (47-XX) 4 General topology (54-XX) 3 Manifolds and cell complexes (57-XX) 2 Real functions (26-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Abstract harmonic analysis (43-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Quantum theory (81-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Potential theory (31-XX) 1 Partial differential equations (35-XX) 1 Mechanics of particles and systems (70-XX)

### Citations contained in zbMATH Open

86 Publications have been cited 1,437 times in 866 Documents Cited by Year
Dynamical properties of some classes of entire functions. Zbl 0735.58031
Eremenko, A.; Lyubich, M.
1992
Entropy properties of rational endomorphisms of the Riemann sphere. Zbl 0537.58035
Lyubich, M. Yu.
1983
Dynamics of quadratic polynomials. I, II. Zbl 0908.58053
Lyubich, Mikhail
1997
Polynomial diffeomorphisms of $$\mathbb{C}^ 2$$. IV: The measure of maximal entropy and laminar currents. Zbl 0792.58034
Bedford, Eric; Lyubich, Mikhail; Smillie, John
1993
Almost every real quadratic map is either regular or stochastic. Zbl 1160.37356
Lyubich, Mikhail
2002
Feigenbaum-Coullet-Tresser universality and Milnor’s hairiness conjecture. Zbl 0945.37012
Lyubich, Mikhail
1999
Laminations in holomorphic dynamics. Zbl 0910.58032
Lyubich, Mikhail; Minsky, Yair
1997
Measurable dynamics of S-unimodal maps of the interval. Zbl 0790.58024
Blokh, A. M.; Lyubich, M. Yu.
1991
The Fibonacci unimodal map. Zbl 0778.58040
Lyubich, Mikhail; Milnor, John
1993
Examples of entire functions with pathological dynamics. Zbl 0601.30033
Eremenko, A. E.; Lyubich, M. Yu.
1987
Regular or stochastic dynamics in real analytic families of unimodal maps. Zbl 1050.37018
Avila, Artur; Lyubich, Mikhail; de Melo, Welington
2003
Combinatorics, geometry and attractors of quasi-quadratic maps. Zbl 0821.58014
Lyubich, Mikhail
1994
Renormalization in the Hénon family. I: Universality but non-rigidity. Zbl 1098.37039
De Carvalho, A.; Lyubich, M.; Martens, M.
2005
The dynamics of rational transforms: the topological picture. Zbl 0619.30033
Lyubich, M. Yu.
1987
The dynamics of analytic transformations. Zbl 0717.58029
Eremenko, A. Eh.; Lyubich, M. Yu.
1990
Distribution of periodic points of polynomial diffeomorphisms of $$\mathbb{C}^ 2$$. Zbl 0799.58039
Bedford, Eric; Lyubich, Mikhail; Smillie, John
1993
Hausdorff dimension and conformal measures of Feigenbaum Julia sets. Zbl 1205.37058
Avila, Artur; Lyubich, Mikhail
2008
Stability and bifurcations for dissipative polynomial automorphisms of $$\mathbb C^2$$. Zbl 1337.37029
Dujardin, Romain; Lyubich, Mikhail
2015
The quasi-additivity law in conformal geometry. Zbl 1203.30011
Kahn, Jeremy; Lyubich, Mikhail
2009
Non-existence of wandering intervals and structure of topological attractors of one dimensional dynamical systems. II: The smooth case. Zbl 0665.58024
Blokh, A. M.; Lyubich, M. Yu.
1989
Some generic properties of the dynamics of rational mappings. Zbl 0546.58033
Lyubich, M. Yu.
1983
Combinatorial rigidity for unicritical polynomials. Zbl 1204.37047
Avila, Artur; Kahn, Jeremy; Lyubich, Mikhail; Shen, Weixiao
2009
Julia sets and complex singularities in hierarchical Ising models. Zbl 0737.30019
Bleher, P. M.; Lyubich, M. Yu.
1991
Dynamics of analytic transformations. Zbl 0712.58036
Eremenko, A. Eh.; Lyubich, M. Yu.
1989
Non-existence of wandering intervals and structure of topological attractors of one dimensional dynamical systems. I: The case of negative Schwarzian derivative. Zbl 0665.58023
Lyubich, M. Yu.
1989
Some typical properties of the dynmics of rational maps. Zbl 0598.58028
Lyubich, M. Yu.
1983
Dynamics of quadratic polynomials: complex bounds for real maps. Zbl 0881.58053
Lyubich, Mikhail; Yampolsky, Michael
1997
Dynamics of quadratic polynomials. III: Parapuzzle and SRB measures. Zbl 1044.37038
Lyubich, Mikhail
2000
Local connectivity of Julia sets for unicritical polynomials. Zbl 1180.37072
Kahn, Jeremy; Lyubich, Mikhail
2009
The full renormalization horseshoe for unimodal maps of higher degree: exponential contraction along hybrid classes. Zbl 1286.37047
Avila, Artur; Lyubich, Mikhail
2011
Renormalization in the Hénon family. II: The heteroclinic web. Zbl 1243.37035
Lyubich, M.; Martens, M.
2011
Classification of invariant Fatou components for dissipative Hénon maps. Zbl 1301.32013
Lyubich, Mikhail; Peters, Han
2014
On typical behavior of the trajectories of a rational mapping of the sphere. Zbl 0595.30034
Lyubich, M. Yu.
1983
Measurable dynamics of the exponential. Zbl 0638.30026
Lyubich, M. Yu.
1987
Conformal and harmonic measures on laminations associated with rational maps. Zbl 1242.37032
2005
Quasisymmetries of Sierpiński carpet Julia sets. Zbl 1358.37083
Bonk, Mario; Lyubich, Mikhail; Merenkov, Sergei
2016
A priori bounds for some infinitely renormalizable quadratics. II: Decorations. Zbl 1156.37311
Kahn, Jeremy; Lyubich, Mikhail
2008
Measure and dimension of solenoidal attractors of one-dimensional dynamical systems. Zbl 0721.58033
Blokh, A. M.; Lyubich, M. Yu.
1990
Lee-Yang zeros for the DHL and 2D rational dynamics. I: Foliation of the physical cylinder. Zbl 1372.82011
Bleher, Pavel; Lyubich, Mikhail; Roeder, Roland
2017
Investigation of the stability of the dynamics of rational functions. Zbl 0572.30023
Lyubich, M. Yu.
1984
Iterates of entire functions. Zbl 0588.30027
Eremenko, A. Eh.; Lyubich, M. Yu.
1984
The quadratic family as a qualitatively solvable model of chaos. Zbl 1040.37032
Lyubich, Mikhail
2000
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.) Zbl 1323.37029
Benini, Anna Miriam; Lyubich, Mikhail
2014
Examples of Feigenbaum Julia sets with small Hausdorff dimension. Zbl 1173.37045
Avila, Artur; Lyubich, Mikhail
2006
Attractors of transformations of a closed interval. Zbl 0653.58022
Blokh, A. M.; Lyubich, M. Yu.
1987
Parapuzzle of the Multibrot set and typical dynamics of unimodal maps. Zbl 1213.37076
Avila, Artur; Lyubich, Mikhail; Shen, Weixiao
2011
Measure of solenoidal attractors of unimodal maps of the segment. Zbl 0774.58026
Blokh, A. M.; Lyubich, M. Yu.
1990
Measurable dynamics of the exponential map. Zbl 0667.58037
Lyubich, M. Yu.
1987
An analysis of the stability of the dynamics of rational functions. Zbl 0697.30026
Lyubich, M. Yu.
1990
Removal of the boundary spectrum for almost periodic operators and representations of semigroups. Zbl 0629.47033
Lyubich, M. Yu.; Lyubich, Yu. I.
1986
Renormalization of Hénon maps. Zbl 1253.37046
Lyubich, M.; Martens, M.
2011
A priori bounds for some infinitely renormalizable quadratics. III: Molecules. Zbl 1180.37069
Kahn, Jeremy; Lyubich, Mikhail
2009
A note on hyperbolic leaves and wild laminations of rational functions. Zbl 1198.30031
Kahn, Jeremy; Lyubich, Mikhail; Rempe, Lasse
2010
Attractors of maps of the interval. Zbl 0698.58037
Blokh, A. M.; Lyubich, M. Yu.
1989
Entropy of analytic endomorphisms of the Riemannian sphere. Zbl 0483.30032
Lyubich, M. Yu.
1982
How big is the set of infinitely renormalizable quadratics? Zbl 0910.58033
Lyubich, Mikhail
1998
Ergodicity of transitive unimodal transformations of a segment. Zbl 0774.58018
Blokh, A. M.; Lyubich, M. Yu.
1989
On decomposition of one-dimensional dynamical systems into ergodic components. The case of negative Schwarzian. Zbl 0718.58024
Blokh, A. M.; Lyubich, M. Yu.
1990
Milnor’s attractors persistent recurrence and renormalization. Zbl 0797.58050
Lyubich, Mikhail
1993
The maximum-entropy measure of a rational endomorphism of the Riemann sphere. Zbl 0525.28021
Lyubich, M. Yu.
1983
A comparison of harmonic and balanced measures on Cantor repellors. Zbl 0891.58024
Lyubich, Mikhail; Volberg, Alexander
1995
Ergodic properties of transformations of an interval. Zbl 0704.58015
Blokh, A. M.; Lyubich, M. Yu.
1989
Renormalization ideas in conformal dynamics. Zbl 0877.58046
Lyubich, Mikhail
1995
Forty years of unimodal dynamics: on the occasion of Artur Avila winning the Brin Prize. Zbl 1280.37036
Lyubich, Mikhail
2012
Lee-Yang-Fisher zeros for the DHL and 2D rational dynamics. II: Global pluripotential interpretation. Zbl 1437.82003
Bleher, Pavel; Lyubich, Mikhail; Roeder, Roland
2020
Teichmüller space of Fibonacci maps. Zbl 1446.37048
Lyubich, Mikhail
2019
On the typical behaviour of trajectories of the exponent. Zbl 0617.30032
Lyubich, M. Yu.
1986
Renormalizable Hénon-like maps and unbounded geometry. Zbl 1268.37060
Hazard, P. E.; Lyubich, M.; Martens, M.
2012
Spectral theory of almost periodic representations of semigroups. Zbl 0557.22006
Lyubich, M. Yu.; Lyubich, Yu. I.
1984
Structural stability in some families of entire functions. Zbl 0597.30032
Eremenko, A. Eh.; Lyubich, M. Yu.
1985
Hedgehogs in higher dimensions and their applications. Zbl 1472.32003
Lyubich, Mikhail; Radu, Remus; Tanase, Raluca
2020
On typical behaviour of trajectories of transformations of a segment. Zbl 0666.58031
Blokh, A. M.; Lyubich, M. Yu.
1988
General form of nonnegative projections in a space of continuous functions on a compactum. Zbl 0685.47033
Lyubich, M. Yu.; Lyubich, Yu. I.
1985
Quasisymmetries of the basilica and the Thompson group. Zbl 06910251
Lyubich, Mikhail; Merenkov, Sergei
2018
Laminations and foliations in dynamics, geometry and topology. Proceedings of the conference held at SUNY at Stony Brook, USA, May 18–24, 1998. Zbl 0959.00033
2001
On the borderline of real and complex dynamics. Zbl 0847.58021
Lyubich, Mikhail
1995
Pacman renormalization and self-similarity of the Mandelbrot set near Siegel parameters. Zbl 1457.37061
Dudko, Dzmitry; Lyubich, Mikhail; Selinger, Nikita
2020
Perron-Frobenius theory for almost periodic operators and representations of semigroups. Zbl 0606.22002
Lyubich, M. Yu.; Lyubich, Yu. I.
1986
Regular and stochastic dynamics in the real quadratic family. Zbl 0936.37020
Lyubich, Mikhail
1998
Absence of wandering intervals in one-dimensional smooth dynamical systems. Zbl 0676.58035
Blokh, A. M.; Lyubich, M. Yu.
1989
Frontiers in complex dynamics. In celebration of John Milnor’s 80th birthday. Based on a conference, Banff, Canada, February 2011. Zbl 1285.37001
2014
Probabilistic universality in two-dimensional dynamics. Zbl 1475.37046
Lyubich, Mikhail Yur’evich; Martens, Marco
2021
Hedgehogs for neutral dissipative germs of holomorphic diffeomorphisms of $$(\mathbb{C}^2,0)$$. Zbl 1478.37052
Firsova, Tanya; Lyubich, Mikhail; Radu, Remus; Tanase, Raluca
2020
Schwarz reflections and anti-holomorphic correspondences. Zbl 1469.30017
Lee, Seung-Yeop; Lyubich, Mikhail; Makarov, Nikolai G.; Mukherjee, Sabyasachi
2021
Structure of partially hyperbolic Hénon maps. Zbl 1470.32042
Lyubich, Mikhail; Peters, Han
2021
Lebesgue measure of Feigenbaum Julia sets. Zbl 1494.37026
Avila, Artur; Lyubich, Mikhail
2022
Lebesgue measure of Feigenbaum Julia sets. Zbl 1494.37026
Avila, Artur; Lyubich, Mikhail
2022
Probabilistic universality in two-dimensional dynamics. Zbl 1475.37046
Lyubich, Mikhail Yur&rsquo;evich; Martens, Marco
2021
Schwarz reflections and anti-holomorphic correspondences. Zbl 1469.30017
Lee, Seung-Yeop; Lyubich, Mikhail; Makarov, Nikolai G.; Mukherjee, Sabyasachi
2021
Structure of partially hyperbolic Hénon maps. Zbl 1470.32042
Lyubich, Mikhail; Peters, Han
2021
Lee-Yang-Fisher zeros for the DHL and 2D rational dynamics. II: Global pluripotential interpretation. Zbl 1437.82003
Bleher, Pavel; Lyubich, Mikhail; Roeder, Roland
2020
Hedgehogs in higher dimensions and their applications. Zbl 1472.32003
Lyubich, Mikhail; Radu, Remus; Tanase, Raluca
2020
Pacman renormalization and self-similarity of the Mandelbrot set near Siegel parameters. Zbl 1457.37061
Dudko, Dzmitry; Lyubich, Mikhail; Selinger, Nikita
2020
Hedgehogs for neutral dissipative germs of holomorphic diffeomorphisms of $$(\mathbb{C}^2,0)$$. Zbl 1478.37052
Firsova, Tanya; Lyubich, Mikhail; Radu, Remus; Tanase, Raluca
2020
Teichmüller space of Fibonacci maps. Zbl 1446.37048
Lyubich, Mikhail
2019
Quasisymmetries of the basilica and the Thompson group. Zbl 06910251
Lyubich, Mikhail; Merenkov, Sergei
2018
Lee-Yang zeros for the DHL and 2D rational dynamics. I: Foliation of the physical cylinder. Zbl 1372.82011
Bleher, Pavel; Lyubich, Mikhail; Roeder, Roland
2017
Quasisymmetries of Sierpiński carpet Julia sets. Zbl 1358.37083
Bonk, Mario; Lyubich, Mikhail; Merenkov, Sergei
2016
Stability and bifurcations for dissipative polynomial automorphisms of $$\mathbb C^2$$. Zbl 1337.37029
Dujardin, Romain; Lyubich, Mikhail
2015
Classification of invariant Fatou components for dissipative Hénon maps. Zbl 1301.32013
Lyubich, Mikhail; Peters, Han
2014
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.) Zbl 1323.37029
Benini, Anna Miriam; Lyubich, Mikhail
2014
Frontiers in complex dynamics. In celebration of John Milnor’s 80th birthday. Based on a conference, Banff, Canada, February 2011. Zbl 1285.37001
2014
Forty years of unimodal dynamics: on the occasion of Artur Avila winning the Brin Prize. Zbl 1280.37036
Lyubich, Mikhail
2012
Renormalizable Hénon-like maps and unbounded geometry. Zbl 1268.37060
Hazard, P. E.; Lyubich, M.; Martens, M.
2012
The full renormalization horseshoe for unimodal maps of higher degree: exponential contraction along hybrid classes. Zbl 1286.37047
Avila, Artur; Lyubich, Mikhail
2011
Renormalization in the Hénon family. II: The heteroclinic web. Zbl 1243.37035
Lyubich, M.; Martens, M.
2011
Parapuzzle of the Multibrot set and typical dynamics of unimodal maps. Zbl 1213.37076
Avila, Artur; Lyubich, Mikhail; Shen, Weixiao
2011
Renormalization of Hénon maps. Zbl 1253.37046
Lyubich, M.; Martens, M.
2011
A note on hyperbolic leaves and wild laminations of rational functions. Zbl 1198.30031
Kahn, Jeremy; Lyubich, Mikhail; Rempe, Lasse
2010
The quasi-additivity law in conformal geometry. Zbl 1203.30011
Kahn, Jeremy; Lyubich, Mikhail
2009
Combinatorial rigidity for unicritical polynomials. Zbl 1204.37047
Avila, Artur; Kahn, Jeremy; Lyubich, Mikhail; Shen, Weixiao
2009
Local connectivity of Julia sets for unicritical polynomials. Zbl 1180.37072
Kahn, Jeremy; Lyubich, Mikhail
2009
A priori bounds for some infinitely renormalizable quadratics. III: Molecules. Zbl 1180.37069
Kahn, Jeremy; Lyubich, Mikhail
2009
Hausdorff dimension and conformal measures of Feigenbaum Julia sets. Zbl 1205.37058
Avila, Artur; Lyubich, Mikhail
2008
A priori bounds for some infinitely renormalizable quadratics. II: Decorations. Zbl 1156.37311
Kahn, Jeremy; Lyubich, Mikhail
2008
Examples of Feigenbaum Julia sets with small Hausdorff dimension. Zbl 1173.37045
Avila, Artur; Lyubich, Mikhail
2006
Renormalization in the Hénon family. I: Universality but non-rigidity. Zbl 1098.37039
De Carvalho, A.; Lyubich, M.; Martens, M.
2005
Conformal and harmonic measures on laminations associated with rational maps. Zbl 1242.37032
2005
Regular or stochastic dynamics in real analytic families of unimodal maps. Zbl 1050.37018
Avila, Artur; Lyubich, Mikhail; de Melo, Welington
2003
Almost every real quadratic map is either regular or stochastic. Zbl 1160.37356
Lyubich, Mikhail
2002
Laminations and foliations in dynamics, geometry and topology. Proceedings of the conference held at SUNY at Stony Brook, USA, May 18–24, 1998. Zbl 0959.00033
2001
Dynamics of quadratic polynomials. III: Parapuzzle and SRB measures. Zbl 1044.37038
Lyubich, Mikhail
2000
The quadratic family as a qualitatively solvable model of chaos. Zbl 1040.37032
Lyubich, Mikhail
2000
Feigenbaum-Coullet-Tresser universality and Milnor’s hairiness conjecture. Zbl 0945.37012
Lyubich, Mikhail
1999
How big is the set of infinitely renormalizable quadratics? Zbl 0910.58033
Lyubich, Mikhail
1998
Regular and stochastic dynamics in the real quadratic family. Zbl 0936.37020
Lyubich, Mikhail
1998
Dynamics of quadratic polynomials. I, II. Zbl 0908.58053
Lyubich, Mikhail
1997
Laminations in holomorphic dynamics. Zbl 0910.58032
Lyubich, Mikhail; Minsky, Yair
1997
Dynamics of quadratic polynomials: complex bounds for real maps. Zbl 0881.58053
Lyubich, Mikhail; Yampolsky, Michael
1997
A comparison of harmonic and balanced measures on Cantor repellors. Zbl 0891.58024
Lyubich, Mikhail; Volberg, Alexander
1995
Renormalization ideas in conformal dynamics. Zbl 0877.58046
Lyubich, Mikhail
1995
On the borderline of real and complex dynamics. Zbl 0847.58021
Lyubich, Mikhail
1995
Combinatorics, geometry and attractors of quasi-quadratic maps. Zbl 0821.58014
Lyubich, Mikhail
1994
Polynomial diffeomorphisms of $$\mathbb{C}^ 2$$. IV: The measure of maximal entropy and laminar currents. Zbl 0792.58034
Bedford, Eric; Lyubich, Mikhail; Smillie, John
1993
The Fibonacci unimodal map. Zbl 0778.58040
Lyubich, Mikhail; Milnor, John
1993
Distribution of periodic points of polynomial diffeomorphisms of $$\mathbb{C}^ 2$$. Zbl 0799.58039
Bedford, Eric; Lyubich, Mikhail; Smillie, John
1993
Milnor’s attractors persistent recurrence and renormalization. Zbl 0797.58050
Lyubich, Mikhail
1993
Dynamical properties of some classes of entire functions. Zbl 0735.58031
Eremenko, A.; Lyubich, M.
1992
Measurable dynamics of S-unimodal maps of the interval. Zbl 0790.58024
Blokh, A. M.; Lyubich, M. Yu.
1991
Julia sets and complex singularities in hierarchical Ising models. Zbl 0737.30019
Bleher, P. M.; Lyubich, M. Yu.
1991
The dynamics of analytic transformations. Zbl 0717.58029
Eremenko, A. Eh.; Lyubich, M. Yu.
1990
Measure and dimension of solenoidal attractors of one-dimensional dynamical systems. Zbl 0721.58033
Blokh, A. M.; Lyubich, M. Yu.
1990
Measure of solenoidal attractors of unimodal maps of the segment. Zbl 0774.58026
Blokh, A. M.; Lyubich, M. Yu.
1990
An analysis of the stability of the dynamics of rational functions. Zbl 0697.30026
Lyubich, M. Yu.
1990
On decomposition of one-dimensional dynamical systems into ergodic components. The case of negative Schwarzian. Zbl 0718.58024
Blokh, A. M.; Lyubich, M. Yu.
1990
Non-existence of wandering intervals and structure of topological attractors of one dimensional dynamical systems. II: The smooth case. Zbl 0665.58024
Blokh, A. M.; Lyubich, M. Yu.
1989
Dynamics of analytic transformations. Zbl 0712.58036
Eremenko, A. Eh.; Lyubich, M. Yu.
1989
Non-existence of wandering intervals and structure of topological attractors of one dimensional dynamical systems. I: The case of negative Schwarzian derivative. Zbl 0665.58023
Lyubich, M. Yu.
1989
Attractors of maps of the interval. Zbl 0698.58037
Blokh, A. M.; Lyubich, M. Yu.
1989
Ergodicity of transitive unimodal transformations of a segment. Zbl 0774.58018
Blokh, A. M.; Lyubich, M. Yu.
1989
Ergodic properties of transformations of an interval. Zbl 0704.58015
Blokh, A. M.; Lyubich, M. Yu.
1989
Absence of wandering intervals in one-dimensional smooth dynamical systems. Zbl 0676.58035
Blokh, A. M.; Lyubich, M. Yu.
1989
On typical behaviour of trajectories of transformations of a segment. Zbl 0666.58031
Blokh, A. M.; Lyubich, M. Yu.
1988
Examples of entire functions with pathological dynamics. Zbl 0601.30033
Eremenko, A. E.; Lyubich, M. Yu.
1987
The dynamics of rational transforms: the topological picture. Zbl 0619.30033
Lyubich, M. Yu.
1987
Measurable dynamics of the exponential. Zbl 0638.30026
Lyubich, M. Yu.
1987
Attractors of transformations of a closed interval. Zbl 0653.58022
Blokh, A. M.; Lyubich, M. Yu.
1987
Measurable dynamics of the exponential map. Zbl 0667.58037
Lyubich, M. Yu.
1987
Removal of the boundary spectrum for almost periodic operators and representations of semigroups. Zbl 0629.47033
Lyubich, M. Yu.; Lyubich, Yu. I.
1986
On the typical behaviour of trajectories of the exponent. Zbl 0617.30032
Lyubich, M. Yu.
1986
Perron-Frobenius theory for almost periodic operators and representations of semigroups. Zbl 0606.22002
Lyubich, M. Yu.; Lyubich, Yu. I.
1986
Structural stability in some families of entire functions. Zbl 0597.30032
Eremenko, A. Eh.; Lyubich, M. Yu.
1985
General form of nonnegative projections in a space of continuous functions on a compactum. Zbl 0685.47033
Lyubich, M. Yu.; Lyubich, Yu. I.
1985
Investigation of the stability of the dynamics of rational functions. Zbl 0572.30023
Lyubich, M. Yu.
1984
Iterates of entire functions. Zbl 0588.30027
Eremenko, A. Eh.; Lyubich, M. Yu.
1984
Spectral theory of almost periodic representations of semigroups. Zbl 0557.22006
Lyubich, M. Yu.; Lyubich, Yu. I.
1984
Entropy properties of rational endomorphisms of the Riemann sphere. Zbl 0537.58035
Lyubich, M. Yu.
1983
Some generic properties of the dynamics of rational mappings. Zbl 0546.58033
Lyubich, M. Yu.
1983
Some typical properties of the dynmics of rational maps. Zbl 0598.58028
Lyubich, M. Yu.
1983
On typical behavior of the trajectories of a rational mapping of the sphere. Zbl 0595.30034
Lyubich, M. Yu.
1983
The maximum-entropy measure of a rational endomorphism of the Riemann sphere. Zbl 0525.28021
Lyubich, M. Yu.
1983
Entropy of analytic endomorphisms of the Riemannian sphere. Zbl 0483.30032
Lyubich, M. Yu.
1982
all top 5

### Cited by 685 Authors

 29 Lyubich, Mikhail 20 Bergweiler, Walter 18 Bruin, Henk 18 van Strien, Sebastian J. 17 Rempe-Gillen, Lasse 16 Tien Cuong Dinh 16 Yampolsky, Michael 14 Martens, Marco 13 Blokh, Alexander M. 13 Cabrera, Carlos 13 Schleicher, Dierk 13 Shen, Weixiao 12 Bedford, Eric 12 Fagella, Núria 12 Peters, Han 12 Yin, Yongcheng 11 Benini, Anna Miriam 11 Dujardin, Romain 11 Oversteegen, Lex G. 11 Przytycki, Feliks 11 Qiu, Weiyuan 11 Sibony, Nessim 11 Urbański, Mariusz 10 de Melo, Welington 10 Gao, Junyang 10 Levin, Genadi M. 10 Makienko, Peter M. 10 Sixsmith, David Jonathan 9 Gaidashev, Denis G. 8 Avila, Artur 8 Berteloot, François 8 Eremenko, Alexandre Émmanuilovich 8 Hawkins, Jane M. 8 Jarque, Xavier 8 Langley, James K. 8 Roeder, Roland K. W. 8 Zdunik, Anna 7 Kawahira, Tomoki 7 Mayer, Volker 7 Okuyama, Yûsuke 7 Qiao, Jianyong 7 Rivera-Letelier, Juan 7 Sienra, Guillermo J. F. 7 Świątek, Grzegorz 7 Wang, Yuefei 7 Yang, Fei 6 Berger, Pierre 6 DeMarco, Laura Grace 6 Palmisano, Liviana 6 Peng, Wenjuan 6 Smillie, John 6 Sridharan, Shrihari 6 Timorin, Vladlen Anatol’evich 6 Zhang, Gaofei 5 Baladi, Viviane 5 Barański, Krzysztof 5 Bianchi, Fabrizio 5 Bishop, Christopher James 5 de Thélin, Henry 5 Domínguez, Patricia 5 Fornæss, John Erik 5 Guarino, Pablo 5 Hurder, Steven E. 5 Koss, Lorelei 5 Lei, Tan 5 Lukina, Olga 5 Prasad, M. Guru Prem 5 Rippon, Philip Jonathan 5 Smania, Daniel 5 Stallard, Gwyneth Mary 5 Taflin, Johan 5 Todd, Mike 5 Yorke, James Alan 5 Young, Lai-Sang 5 Zeng, Jinsong 5 Zhai, Yu 4 Boc Thaler, Luka 4 Cantat, Serge 4 Chandramouli, V. V. M. S. 4 Clark, Alex 4 Clark, Trevor 4 Damanik, David 4 Devaney, Robert L. 4 Diller, Jeffrey 4 Dobbs, Neil B. 4 Dudko, Artem 4 Dupont, Christophe 4 Evdoridou, Vasiliki 4 Filip, Simion 4 Galias, Zbigniew 4 Gauthier, Thomas 4 Graczyk, Jacek 4 Guedj, Vincent 4 Hubbard, John Hamal 4 Iommi, Godofredo 4 Jiménez López, Víctor 4 Kim, Kyounghee 4 Luzzatto, Stefano 4 Martí-Pete, David 4 McMullen, Curtis Tracy ...and 585 more Authors
all top 5

### Cited in 167 Serials

 59 Ergodic Theory and Dynamical Systems 50 Transactions of the American Mathematical Society 42 Communications in Mathematical Physics 32 Proceedings of the American Mathematical Society 31 Conformal Geometry and Dynamics 28 Advances in Mathematics 24 Inventiones Mathematicae 22 Journal of Mathematical Analysis and Applications 19 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 17 Discrete and Continuous Dynamical Systems 16 Mathematische Annalen 16 The Journal of Geometric Analysis 15 Journal d’Analyse Mathématique 15 Mathematische Zeitschrift 12 Israel Journal of Mathematics 12 Annales de l’Institut Fourier 12 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 11 Journal of the American Mathematical Society 11 Science China. Mathematics 10 Journal of Statistical Physics 10 Mathematical Proceedings of the Cambridge Philosophical Society 10 Duke Mathematical Journal 10 Topology and its Applications 10 Journal of the European Mathematical Society (JEMS) 9 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 9 Chaos 9 Computational Methods and Function Theory 9 Arnold Mathematical Journal 8 Acta Mathematica 8 Geometric and Functional Analysis. GAFA 8 Dynamical Systems 8 Journal of Modern Dynamics 7 Indian Journal of Pure & Applied Mathematics 7 Nonlinearity 7 Science in China. Series A 7 Bulletin of the American Mathematical Society. New Series 7 Journal of Difference Equations and Applications 7 Annals of Mathematics. Second Series 6 Arkiv för Matematik 6 Chaos, Solitons and Fractals 6 International Journal of Mathematics 6 Journal of Dynamics and Differential Equations 6 Annales Academiae Scientiarum Fennicae. Mathematica 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 Fundamenta Mathematicae 5 Physica D 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 5 Experimental Mathematics 5 Complex Analysis and Operator Theory 4 Journal of Mathematical Physics 4 Illinois Journal of Mathematics 4 Journal of the London Mathematical Society. Second Series 4 Acta Mathematica Sinica. English Series 4 Complex Variables and Elliptic Equations 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Publications Mathématiques 3 Journal of Soviet Mathematics 3 Memoirs of the American Mathematical Society 3 Michigan Mathematical Journal 3 Monatshefte für Mathematik 3 Tôhoku Mathematical Journal. Second Series 3 Publicacions Matemàtiques 3 Annales de l’Institut Henri Poincaré. Physique Théorique 3 Acta Mathematica Sinica. New Series 3 Indagationes Mathematicae. New Series 3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 3 Annales Henri Poincaré 3 Qualitative Theory of Dynamical Systems 2 Bulletin of the Australian Mathematical Society 2 Mathematical Notes 2 Rocky Mountain Journal of Mathematics 2 Journal of Differential Equations 2 Journal of Functional Analysis 2 Journal of Number Theory 2 Nagoya Mathematical Journal 2 Proceedings of the Japan Academy. Series A 2 Results in Mathematics 2 Theoretical Computer Science 2 Bulletin of the Korean Mathematical Society 2 Chinese Annals of Mathematics. Series B 2 IMRN. International Mathematics Research Notices 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Chinese Science Bulletin 2 Potential Analysis 2 Geometry & Topology 2 Journal of the Australian Mathematical Society 2 Stochastics and Dynamics 2 Advances in Difference Equations 2 Journal of Fixed Point Theory and Applications 2 Frontiers of Mathematics in China 2 Groups, Geometry, and Dynamics 2 Analysis and Mathematical Physics 2 Communications in Mathematics and Statistics 2 Journal of Fractal Geometry 1 Communications on Pure and Applied Mathematics 1 Mathematical Biosciences 1 Physics Letters. A 1 Reviews in Mathematical Physics 1 Acta Mathematica Vietnamica 1 American Journal of Mathematics ...and 67 more Serials
all top 5

### Cited in 40 Fields

 761 Dynamical systems and ergodic theory (37-XX) 279 Functions of a complex variable (30-XX) 120 Several complex variables and analytic spaces (32-XX) 39 Measure and integration (28-XX) 25 General topology (54-XX) 24 Statistical mechanics, structure of matter (82-XX) 23 Probability theory and stochastic processes (60-XX) 19 Number theory (11-XX) 18 Algebraic geometry (14-XX) 18 Difference and functional equations (39-XX) 18 Manifolds and cell complexes (57-XX) 16 Group theory and generalizations (20-XX) 15 Ordinary differential equations (34-XX) 11 Global analysis, analysis on manifolds (58-XX) 11 Numerical analysis (65-XX) 10 Operator theory (47-XX) 9 Potential theory (31-XX) 8 Real functions (26-XX) 7 Combinatorics (05-XX) 7 Differential geometry (53-XX) 6 Partial differential equations (35-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 5 Special functions (33-XX) 5 Abstract harmonic analysis (43-XX) 5 Computer science (68-XX) 5 Mechanics of particles and systems (70-XX) 5 Quantum theory (81-XX) 5 Biology and other natural sciences (92-XX) 4 General and overarching topics; collections (00-XX) 4 Functional analysis (46-XX) 3 Mathematical logic and foundations (03-XX) 3 Topological groups, Lie groups (22-XX) 2 Convex and discrete geometry (52-XX) 2 Statistics (62-XX) 2 Operations research, mathematical programming (90-XX) 2 Information and communication theory, circuits (94-XX) 1 Commutative algebra (13-XX) 1 Sequences, series, summability (40-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Fluid mechanics (76-XX)

### Wikidata Timeline

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.