Positions

Selected Publications

Academic Article

Year Title Altmetric
2019 Models for spaces of dendritic polynomialsTransactions of the American Mathematical Society.  372:4829-4849. 2019
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 setsPsychonomic science.  37:5781-5795. 2017
2017 Combinatorial models for spaces of cubic polynomialsCurrent Opinion in Infectious Diseases.  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 cubioidPsychonomic science.  36:4665-4702. 2016
2016 Quadratic-Like Dynamics of Cubic PolynomialsCardiovascular Ultrasound.  341:733-749. 2016
2016 An extended Fatou-Shishikura inequality and wandering branch continua for polynomialsBulletin de l'Académie Nationale de Médecine.  288:1121-1174. 2016
2015 The combinatorial Mandelbrot set as the quotient of the space of geolaminationsCancer Genomics and Proteomics2015
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 portraitsPsychonomic science.  32:2027-2039. 2012
2011 Topological polynomials with a simple coreIEEE Transactions on Vehicular Technology2011
2011 Non-degenerate quadratic laminationsTopology Proceedings.  38:313-360. 2011
2011 Locally connected models for Julia setsBulletin de l'Académie Nationale de Médecine.  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 mapsCardiovascular Ultrasound.  289:765-776. 2009
2009 The julia sets of basic unicremer polynomials of arbitrary degreeIn S. H. Johnson (Ed.), High Risk Parenting, 2nd Ed. Philadelphia: Lippincott.  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 obstacleCardiovascular Ultrasound.  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 laminationsPsychonomic science.  13:13-34. 2005
2004 Wandering triangles existCurrent Opinion in Infectious Diseases.  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?Psychonomic science.  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 setsPsychonomic science.  4:141-158. 1998
1998 Collet-Eckmann maps are unstableCardiovascular Ultrasound.  191:61-70. 1998
1998 Wild attractors of polymodal negative Schwarzian mapsCardiovascular Ultrasound.  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 cyclesTamkang Journal of Science and Engineering.  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 mapsCollege Teaching1991
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 systemsCardiovascular Ultrasound.  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
Slices of Parameter Space of Cubic Polynomials

Chapter

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

Teaching Activities

  • MA125 - Calculus I (Fall Term 2019) 2019
  • MA490 - Mathematics Seminar (Fall Term 2019) 2019
  • MA793 - Special Topics in Mathematics (Fall Term 2019) 2019
  • MA798 - Non-Diss Research/Comp Prep (Fall Term 2019) 2019
  • MA125 - Calculus I (Summer Term 2019) 2019
  • MA126 - Calculus II (Summer Term 2019) 2019
  • MA693 - Special Topics in Mathematics (Summer Term 2019) 2019
  • MA793 - Special Topics in Mathematics (Summer Term 2019) 2019
  • MA125 - Calculus I (Spring Term 2019) 2019
  • MA490 - Mathematics Seminar (Spring Term 2019) 2019
  • MA798 - Non-Diss Research/Comp Prep (Spring Term 2019) 2019
  • MA125 - Calculus I (Fall Term 2018) 2018
  • MA490 - Mathematics Seminar (Fall Term 2018) 2018
  • MA798 - Non-Diss Research/Comp Prep (Fall Term 2018) 2018
  • MA125 - Calculus I (Summer Term 2018) 2018
  • MA671 - Topology II (Summer Term 2018) 2018
  • MA798 - Non-Diss Research/Comp Prep (Summer Term 2018) 2018
  • MA125 - Calculus I (Spring Term 2018) 2018
  • MA490 - Mathematics Seminar (Spring Term 2018) 2018
  • MA695 - Special Topics in Mathematics (Spring Term 2018) 2018
  • MA125 - Calculus I (Fall Term 2017) 2017
  • MA125 - Calculus I (Fall Term 2017) 2017
  • MA490 - Mathematics Seminar (Fall Term 2017) 2017
  • MA798 - Non-Diss Research/Comp Prep (Fall Term 2017) 2017
  • MA126 - Calculus II (Summer Term 2017) 2017
  • MA671 - Topology II (Summer Term 2017) 2017
  • MA693 - Special Topics in Mathematics (Summer Term 2017) 2017
  • MA125 - Calculus I (Spring Term 2017) 2017
  • MA490 - Mathematics Seminar (Spring Term 2017) 2017
  • MA125 - Calculus I (Fall Term 2016) 2016
  • MA490 - Mathematics Seminar (Fall Term 2016) 2016
  • MA126 - Calculus II (Summer Term 2016) 2016
  • MA126 - Calculus II (Summer Term 2016) 2016
  • MA125 - Calculus I (Spring Term 2016) 2016
  • MA125 - Calculus I (Fall Term 2015) 2015
  • MA125 - Calculus I (Fall Term 2015) 2015
  • MA398 - Research in Mathematics (Fall Term 2015) 2015
  • MA490 - Mathematics Seminar (Fall Term 2015) 2015
  • MA491 - Special Topics in Mathematics (Fall Term 2015) 2015
  • MA693 - Special Topics in Mathematics (Fall Term 2015) 2015
  • MA793 - Special Topics in Mathematics (Fall Term 2015) 2015
  • MA126 - Calculus II (Summer Term 2015) 2015
  • MA298 - Research in Mathematics (Summer Term 2015) 2015
  • MA398 - Research in Mathematics (Summer Term 2015) 2015
  • MA494 - Special Topics in Mathematics (Summer Term 2015) 2015
  • MA671 - Topology II (Summer Term 2015) 2015
  • MA691 - Mathematics Seminar (Summer Term 2015) 2015
  • MA793 - Special Topics in Mathematics (Summer Term 2015) 2015
  • MA126 - Calculus II (Spring Term 2015) 2015
  • MA474 - Intro to Topology I (Spring Term 2015) 2015
  • MA490 - Mathematics Seminar (Spring Term 2015) 2015
  • MA494 - Special Topics in Mathematics (Spring Term 2015) 2015
  • MA670 - Topology I (Spring Term 2015) 2015
  • MA693 - Special Topics in Mathematics (Spring Term 2015) 2015
  • MA794 - Special Topics in Mathematics (Spring Term 2015) 2015
  • MA125 - Calculus I (Fall Term 2014) 2014
  • MA490 - Mathematics Seminar (Fall Term 2014) 2014
  • MA491 - Mathematics Senior Seminar (Fall Term 2014) 2014
  • MA692 - Special Topics in Mathematics (Fall Term 2014) 2014
  • MA125 - Calculus I (Spring Term 2014) 2014
  • MA125 - Calculus I (Fall Term 2013) 2013
  • MA125 - Calculus I (Fall Term 2013) 2013
  • MA125 - Calculus I (Spring Term 2013) 2013
  • MA125 - Calculus I (Fall Term 2012) 2012
  • MA125 - Calculus I (Fall Term 2012) 2012
  • MA671 - Topology II (Summer Term 2012) 2012
  • MA490 - Mathematics Seminar (Spring Term 2012) 2012
  • MA670 - Topology I (Spring Term 2012) 2012
  • MA125 - Calculus I (Fall Term 2011) 2011
  • MA361 - Mathematical Modeling (Fall Term 2011) 2011
  • MA490 - Mathematics Seminar (Fall Term 2011) 2011
  • MA519 - Special Topics for Teachers (Fall Term 2011) 2011
  • MA490 - Mathematics Seminar (Summer Term 2011) 2011
  • MA125 - Calculus I (Spring Term 2011) 2011
  • MA490 - Mathematics Seminar (Spring Term 2011) 2011
  • MA109 - Survey of Calculus (Fall Term 2010) 2010
  • MA109 - Survey of Calculus (Fall Term 2010) 2010
  • MA125 - Calculus I (Fall Term 2010) 2010
  • MA490 - Mathematics Seminar (Fall Term 2010) 2010
  • MA490 - Mathematics Seminar (Summer Term 2010) 2010
  • MA126 - Calculus II (Spring Term 2010) 2010
  • MA490 - Mathematics Seminar (Spring Term 2010) 2010
  • MA126 - Calculus II (Fall Term 2009) 2009
  • MA490 - Mathematics Seminar (Fall Term 2009) 2009
  • MA692 - Special Topics in Mathematics (Fall Term 2009) 2009
  • MA126 - Calculus II (Fall Term 2008) 2008
  • MA772 - Complex Analytic Dynamics (Fall Term 2008) 2008
  • MA109 - Survey of Calculus (Summer Term 2008) 2008
  • MA670 - Topology I (Spring Term 2008) 2008
  • MA109 - Survey of Calculus (Fall Term 2007) 2007
  • MA109 - Survey of Calculus (Fall Term 2007) 2007
  • Education And Training

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

  • Alexander Blokh