Positions

Selected Publications

Academic Article

Year Title Altmetric
2018 Perfect subspaces of quadratic laminationsScience in China Series A: Mathematics.  61:2121-2138. 2018
2018 Complementary components to the cubic principal hyperbolic domainProceedings of the American Mathematical Society.  146:4649-4660. 2018
2017 Non-degenerate locally connected models for plane continua and julia setsDiscrete and Continuous Dynamical Systems - Series A.  37:5781-5795. 2017
2017 Combinatorial models for spaces of cubic polynomialsComptes Rendus- Academie des Sciences Paris Serie 1.  355:590-595. 2017
2017 The parameter space of cubic laminations with a fixed critical leafErgodic Theory and Dynamical Systems.  37:2453-2486. 2017
2016 Laminations from the main cubioidDiscrete and Continuous Dynamical Systems - Series A.  36:4665-4702. 2016
2016 Quadratic-Like Dynamics of Cubic PolynomialsCommunications in Mathematical Physics.  341:733-749. 2016
2016 An extended Fatou-Shishikura inequality and wandering branch continua for polynomialsAdvances in Mathematics.  288:1121-1174. 2016
2015 The combinatorial Mandelbrot set as the quotient of the space of geolaminationsContemporary Mathematics, v. 669 (2016), 37-622015
2015 Pointwise-recurrent maps on uniquely arcwise connected locally arcwise connected spacesProceedings of the American Mathematical Society.  143:3985-4000. 2015
2014 The main cubioidNonlinearity.  27:1879-1897. 2014
2014 Laminational models for some spaces of polynomials of any degree 2014
2013 Recurrent and periodic points in dendritic Julia setsProceedings of the American Mathematical Society.  141:3587-3599. 2013
2013 Laminations in the language of leavesTransactions of the American Mathematical Society.  365:5367-5391. 2013
2013 Fixed point theorems for plane continua with applicationsMemoirs of the American Mathematical Society.  224:1-117. 2013
2013 Over-rotation numbers for unimodal mapsJournal of Difference Equations and Applications.  19:1108-1132. 2013
2013 Cubic critical portraits and polynomials with wandering gapsErgodic Theory and Dynamical Systems.  33:713-738. 2013
2013 Finitely suslinian models for planar compacta with applications to julia setsProceedings of the American Mathematical Society.  141:1437-1440. 2013
2012 Density of orbits in laminations and the space of critical portraitsDiscrete and Continuous Dynamical Systems - Series A.  32:2027-2039. 2012
2011 Topological polynomials with a simple core"Frontiers in Complex Dynamics (Celebrating John Milnor's 80th birthday)'', Princeton University Press (2013), 27-472011
2011 Non-degenerate quadratic laminationsTopology Proceedings.  38:313-360. 2011
2011 Locally connected models for Julia setsAdvances in Mathematics.  226:1621-1661. 2011
2010 Monotone images of cremer julia setsHOUSTON JOURNAL OF MATHEMATICS.  36:469-476. 2010
2010 The solar Julia sets of basic quadratic Cremer polynomialsErgodic Theory and Dynamical Systems.  30:51-65. 2010
2009 Local critical perturbations of unimodal mapsCommunications in Mathematical Physics.  289:765-776. 2009
2009 The julia sets of basic unicremer polynomials of arbitrary degreeConformal Geometry and Dynamics.  13:139-159. 2009
2009 Sets of constant distance from a compact set in 2-manifolds with a geodesic metricProceedings of the American Mathematical Society.  137:733-743. 2009
2009 A fixed point theorem for branched covering maps of the planeFundamenta Mathematicae.  206:77-111. 2009
2009 Asymptotic behaviour of the entropy of interval mapsJournal of Difference Equations and Applications.  15:1-11. 2009
2008 Fixed points in non-invariant plane continua 2008
2007 Planar finitely suslinian compactaProceedings of the American Mathematical Society.  135:3755-3764. 2007
2006 On almost one-to-one mapsTransactions of the American Mathematical Society.  358:5003-5014. 2006
2006 The Julia sets of quadratic Cremer polynomialsTopology and its Applications.  153:3038-3050. 2006
2006 Rotation sets of billiards with one obstacleCommunications in Mathematical Physics.  266:239-265. 2006
2006 Applications of almost one-to-one mapsTopology and its Applications.  153:1571-1585. 2006
2006 Rotational subsets of the circle under zdTopology and its Applications.  153:1540-1570. 2006
2005 Julia sets of expanding polymodialsErgodic Theory and Dynamical Systems.  25:1691-1718. 2005
2005 Attractors and recurrence for dendrite-critical polynomialsJournal of Mathematical Analysis and Applications.  306:567-588. 2005
2005 Branched derivativesNonlinearity.  18:703-715. 2005
2005 On minimal maps of 2-manifoldsErgodic Theory and Dynamical Systems.  25:41-57. 2005
2005 Necessary conditions for the existence of wandering triangles for cubic laminationsDiscrete and Continuous Dynamical Systems - Series A.  13:13-34. 2005
2004 Wandering triangles existComptes Rendus- Academie des Sciences Paris Serie 1.  339:365-370. 2004
2004 Backward stability for polynomial maps with locally connected Julia setsTransactions of the American Mathematical Society.  356:119-133. 2004
2003 How little is little enough?Discrete and Continuous Dynamical Systems - Series A.  9:969-978. 2003
2003 Erratum: Typical limit sets of critical points for smooth interval maps (Ergodic Theory and Dynamical System (2000) 20 (15-45))Ergodic Theory and Dynamical Systems.  23:661. 2003
2003 On graph-realizable sets of periodsJournal of Difference Equations and Applications.  9:343-357. 2003
2002 Sets that force recurrenceProceedings of the American Mathematical Society.  130:3571-3578. 2002
2002 An inequality for laminations, Julia sets and 'growing trees'Ergodic Theory and Dynamical Systems.  22:63-97. 2002
2002 On dynamics of vertices of locally connected polynomial Julia setsProceedings of the American Mathematical Society.  130:3219-3230. 2002
2002 Attractors for graph critical rational mapsTransactions of the American Mathematical Society.  354:3639-3661. 2002
2001 Rotation numbers for certain maps of an n-odTopology and its Applications.  114:27-48. 2001
2000 Recurrent critical points and typical limit sets for conformal measuresTopology and its Applications.  108:233-244. 2000
2000 Typical limit sets of critical points for smooth interval mapsErgodic Theory and Dynamical Systems.  20:15-45. 2000
1999 Recurrent critical points and typical limit sets of rational mapsProceedings of the American Mathematical Society.  127:1215-1220. 1999
1999 Rotating an interval and a circleTransactions of the American Mathematical Society.  351:63-78. 1999
1998 Dense set of negative Schwarzian maps whose critical points have minimal limit setsDiscrete and Continuous Dynamical Systems - Series A.  4:141-158. 1998
1998 Collet-Eckmann maps are unstableCommunications in Mathematical Physics.  191:61-70. 1998
1998 Wild attractors of polymodal negative Schwarzian mapsCommunications in Mathematical Physics.  199:397-416. 1998
1997 Entropy of twist interval mapsIsrael Journal of Mathematics.  102:61-99. 1997
1997 New order for periodic orbits of interval mapsErgodic Theory and Dynamical Systems.  17:565-574. 1997
1996 The space of ω-limit sets of a continuous map of the intervalTransactions of the American Mathematical Society.  348:1357-1372. 1996
1996 Sharkovskiǐ type of cyclesBulletin of the London Mathematical Society.  28:417-424. 1996
1995 OPEN PROBLEMS SESSIONInternational Journal of Bifurcation and Chaos.  05:1303-1305. 1995
1995 Functional rotation numbers for one-dimensional mapsTransactions of the American Mathematical Society.  347:499-513. 1995
1995 Rotation numbers, twists and a Sharkovskii–Misiurewicz-type ordering for patterns on the intervalErgodic Theory and Dynamical Systems.  15:1-14. 1995
1994 On rotation intervals for interval mapsNonlinearity.  7:1395-1417. 1994
1994 Trees with snowflakes and zero entropy mapsTopology.  33:379-396. 1994
1992 Periods implying almost all periods for tree mapsNonlinearity.  5:1375-1382. 1992
1992 The set of all iterates is nowhere dense in c([0, 1], [0, 1])Transactions of the American Mathematical Society.  333:787-798. 1992
1991 The "spectral" decomposition for one-dimensional mapsDynamics Reported 4 (1995), 1-591991
1991 Periods implying almost all periods, trees with snowflakes, and zero entropy mapsTopology , #2 33 (1994), 379-396; Nonlineraity 5 (1992), 1375-13821991
1990 Measure of solenoidal attractors of unimodal maps of the segmentMatematicheskie Zametki / Mathematical Notes.  48:1085-1090. 1990
1990 On dynamical systems on one-dimensional branched manifolds. IIIJournal of Mathematical Sciences.  49:875-883. 1990
1990 Typical behavior of the trajectories of transformations of a segmentJournal of Mathematical Sciences.  49:1037-1044. 1990
1990 Dynamical systems on one-dimensional branched manifolds. IIJournal of Mathematical Sciences.  48:668-674. 1990
1990 Dynamical systems on one-dimensional branched manifolds. IJournal of Mathematical Sciences.  48:500-508. 1990
1990 Measure and dimension of solenoidal attractors of one dimensional dynamical systemsCommunications in Mathematical Physics.  127:573-583. 1990
1989 Ergodicity of transitive unimodal transformations of a segmentUkrainian Mathematical Journal.  41:841-844. 1989
1989 Ergodic properties of transformations of an intervalFunctional Analysis and Its Applications.  23:48-49. 1989
1989 Non-existence of wandering intervals and structure of topological attractors of one dimensional dynamical systems 2. The smooth caseErgodic Theory and Dynamical Systems.  9:751-758. 1989
1987 Letter to the editorRussian Mathematical Surveys.  42:249. 1987
1987 On the connection between entropy and transitivity for one-dimensional mappingsRussian Mathematical Surveys.  42:165-166. 1987
1987 Attractors of transformations of an intervalFunctional Analysis and Its Applications.  21:148-150. 1987
1983 Decomposition of dynamical systems on an intervalRussian Mathematical Surveys.  38:133-134. 1983
1982 On the "spectral decomposition" for piecewise-monotone maps of segmentsRussian Mathematical Surveys.  37:198-199. 1982
1982 On sensitive mappings of the intervalRussian Mathematical Surveys.  37:203-204. 1982
1982 On the limit behaviour of one-dimensional dynamical systemsRussian Mathematical Surveys.  37:157-158. 1982
1969 Experience with the use of computers in the diagnosis of multiple sclerosisZhurnal nevropatologii i psikhiatrii imeni S.S. Korsakova (Moscow, Russia : 1952).  69:1624-1628. 1969
Forcing among patterns with no block structureTopology Proceedings, vol. 54 (2019), 125-137
Location of Siegel capture polynomials in parameter spaces
Models for spaces of dendritic polynomials
Slices of Parameter Space of Cubic Polynomials

Chapter

Year Title Altmetric
2014 Dynamical cores of topological polynomials.  27-48. 2014

Teaching Activities

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  • Education And Training

  • Doctor of Philosophy in Mathematics, Voronezh State University 1985
  • Full Name

  • Alexander Blokh