Alexander Blokh
Department of Mathematics
University of Alabama at Birmingham
Birmingham, Alabama 35294
E-mail: ablokh@math.uab.edu
Fax: (205) 934-9025
Telephone: (205) 934-2154

PUBLICATIONS

(See reviews in Mathematical Reviews)

Refereed papers

A. Blokh, L. Oversteegen, V. Timorin
Perfect subspaces of quadratic laminations,
29 pages, 4 figures, submitted (2017), paper in PDF (1,096K)

A. Blokh, L. Oversteegen, R. Ptacek, V. Timorin
Combinatorial models for spaces of cubic polynomials,
C. R. Math. (Acad. Sci., Paris), 355 (2017), issue 5, 590-595, paper in PDF (172K)

A. Blokh, L. Oversteegen, R. Ptacek, V. Timorin
Models for spaces of dendritic polynomials,
22 pages, 2 figures, submitted (2017), paper in PDF (172K)

A. Blokh, L. Oversteegen, R. Ptacek, V. Timorin
Laminational models for some spaces of polynomials of arbitrary degree,
102 pages, 13 figures, to appear in Memoirs of the AMS , paper in PDF (636K)

A. Blokh, L. Oversteegen, V. Timorin
Slices of the Parameter Space of Cubic Polynomials,
60 pages, 3 figures, submitted (2016), paper in PDF (813K)

A. Blokh, L. Oversteegen, V. Timorin
Non-degenerate locally connected models for plane continua and Julia sets,
Discrete and Continuous Dynamical Systems - Series A , 37 (2017), 5781-5795, paper in PDF (380K)

A. Blokh, L. Oversteegen, R. Ptacek, V. Timorin
The combinatorial Mandelbrot set as the quotient of the space of geolaminations,
Contemporary Mathematics , 669 (2016), 37-62, paper in PDF (821K)

A. Blokh, L. Oversteegen, R. Ptacek, V. Timorin
The parameter space of cubic laminations with a fixed critical leaf,
40 pages, 2 figures (2015), to appear in Ergodic Theory and Dynamical Systems, paper in PDF (392K)

A. Blokh, L. Oversteegen, R. Ptacek, V. Timorin
Complementary components to the cubic principal domain,
(2014), 12 pages, 1 figure, to appear in Proc. Amer. Math. Soc. , paper in PDF (133K)

A. Blokh
Pointwise-recurrent maps on uniquely arcwise connected locally arcwise connected spaces,
Proc. Amer. Math. Soc. 143 (2015), 3985-4000, paper in PDF (356K)

A. Blokh, L. Oversteegen, R. Ptacek, V. Timorin
Laminations from the Main Cubioid,
38 pages, Discrete and Continuous Dynamical Systems - Series A , 36 (2016), 4665-4702,
paper in PDF (647K)

A. Blokh, L. Oversteegen, R. Ptacek, V. Timorin
Quadratic-like dynamics of cubic polynomials,
Communications in Mathematical Physics , 341 (2016), 733-749,
paper in PDF (383K)

A. Blokh, L. Oversteegen, R. Ptacek, V. Timorin
The Main Cubioid,
Nonlinearity, 27 (2014), 1879-1897,
paper in PDF (186K)

A. Blokh, K. Snider
Over-rotation numbers for unimodal maps,
Journal of Difference Equations and Applications, 19 (2013), 1108-1132
paper in PDF (217K)

A. Blokh
Recurrent and periodic points in dendritic Julia sets,
Proc. Amer. Math. Soc., 141 (2013), 3587-3599
paper in PDF (318K)

A. Blokh, L. Oversteegen, R. Ptacek, V. Timorin
Dynamical cores of topological polynomials,
Proceedings for the Conference ``Frontiers in Complex Dynamics (Celebrating John Milnor's 80th birthday)'',
edited by Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland
Princeton Mathematical Series 51, Princeton University Press (2013), 27-47
paper in PDF (360K)

A. Blokh, D. Mimbs, L. Oversteegen, K. Valkenburg
Laminations in the language of leaves,
Trans. Amer. Math. Soc. , 365 (2013), 5367-5391
paper in PDF (600K)

A. Blokh, C. Curry, L. Oversteegen
Finitely Suslinian models for planar compacta with applications to Julia sets,
Proc. Amer. Math. Soc., 141 (2013), 1437-1449
paper in PDF (181K)

A. Blokh, D. Childers, G. Levin, L. Oversteegen, D. Schleicher
An Extended Fatou-Shishikura inequality and wandering branch continua for polynomials,
Advances in Mathematics , 288 (2016), 1121-1174
paper in PDF(1,100K)

A. Blokh, R. Fokkink, J. Mayer, L. Oversteegen, E. Tymchatyn
Fixed point theorems for plane continua with applications,
Memoirs of the AMS, 224 (2013), no. 1053, 110 pages,
paper in PDF (750K)

A. Blokh, C. Curry, L. Oversteegen
Cubic Critical Portraits and Polynomials with Wandering Gaps,
Ergodic Theory and Dynamical Systems , 33 (2013), 713--738
paper in PDF (732K)

A. Blokh, C. Curry, L. Oversteegen
Density of orbits in laminations and the space of critical portraits,
Disc. and Cont. Dyn. Syst. 32 (2012), 2027--2039
PDF (131K)

A. Blokh, D. Childers, J. Mayer, L. Oversteegen
Non-degenerate quadratic laminations,
Topology Proceedings, 38 (2011), 313-360, PDF (338K)

A. Blokh, C. Curry, L. Oversteegen
Locally connected models for Julia sets,
Advances in Mathematics, 226 (2011), 1621-1661, PDF (402K)

A. Blokh, X. Buff, A. Cheritat, L. Oversteegen
The solar Julia sets of basic quadratic Cremer polynomials,
Ergodic Theory and Dynamical Systems , 30 (2010), #1, 51-65, PDF (357K)

A. Blokh, L. Oversteegen
Monotone images of Cremer Julia sets,
Houston Journal of Mathematics, 36 (2010), 469--476, PDF (170K)

A. Blokh, M. Misiurewicz
Local critical perturbations of unimodal maps,
Comm. Math. Phys. , 289 (2009), 765-776, PDF (282K)

A. Blokh, J. Bobok
Asymptotic behavior of the entropy of interval maps,
Jour. of Diff. Eq. Appl. , 15 (2009), #1, 1-11, PDF (200K)

A. Blokh, L. Oversteegen
The Julia sets of basic uniCremer polynomials of arbitrary degree,
Conformal Geometry and Dynamics , 13 (2009), 139-159, PDF (282K)

A. Blokh, L. Oversteegen
A fixed point theorem for branched covering maps of the plane
Fundamenta Mathematicae , 206 (2009), 77-111, PDF (323K)

A. Blokh, M. Misiurewicz, L. Oversteegen
Sets of constant distance from a compact set in 2-manifolds with a geodesic metric,
Proc. Amer. Math. Soc. , 137 (2009), 733--743, PDF (178K)

A. Blokh, L. Oversteegen
Wandering Gaps for Weakly Hyperbolic Polynomials,
in: ``Complex dynamics: families and friends'', ed. by D. Schleicher,
A K Peters (2008), pp. 139--168, PDF (295K)

A. Blokh, M. Misiurewicz, L. Oversteegen
Planar finitely Suslinian compacta,
Proc. Amer. Math. Soc.
, 135 (2007), 3755--3764, PDF (194K)

A. Blokh, L. Oversteegen
The Julia sets of quadratic Cremer polynomials,
Topology and its Appl.
, 153 (2006), 3038--3050, PDF (295K)

A. Blokh, M. Misiurewicz, N. Simanyi
Rotation sets of billiards with one obstacle,
Comm. Math. Phys.
266 (2006), #1, 239--265, PDF (323K)

A. Blokh, J. Malaugh, J. Mayer, L. Oversteegen, D. Parris
Rotational subsets of the circle under zn,
Topology and its Appl.
, 153 (2006), 1540--1570, PDF (295K)

A. Blokh, L. Oversteegen, E. Tymchatyn
On almost one-to-one maps,
Trans. Amer. Math. Soc.
, 358 (2006), #11, 5003--5014, PDF (207K)

A. Blokh, L. Oversteegen, E. Tymchatyn
Applications of almost one-to-one maps,
Topology and its Appl.
153 (2006), 1571--1585, PDF (207K)

A. Blokh, M. Misiurewicz
Branched derivatives,
Nonlinearity
, 18 (2005), 703--715, PDF (335K)

A. Blokh, L. Oversteegen, E. Tymchatyn
On minimal maps of 2-manifolds,
Ergodic Theory and Dynamical Systems
, 25 (2005), #1, 41--57, PDF (220K)

A. Blokh, M. Misiurewicz
Attractors and recurrence for dendrite-critical polynomials,
Journal of Mathematical Analysis and Applications
, 306 (2005), 567--588, PDF (279K)

A. Blokh, C. Cleveland, M. Misiurewicz
Julia sets of expanding polymodials,
Ergodic Theory and Dynamical Systems
, 25 (2005), no. 5, 1691-1718, PS (567K)

A. Blokh
Necessary conditions for the existence of wandering vertices for cubic laminations,
Disc. and Cont. Dyn. Syst.
, 13 (2005), 13--34, PDF (280K)

A. Blokh, C. Cleveland, M. Misiurewicz
Expanding polymodials
in: Modern Dynamics and Applications, (M. Brin, B. Haselblatt, and Y. Pesin, eds.),
Cambridge University Press, London (2004), pp. 253-270, PDF (350K)

A. Blokh, L. Oversteegen
Wandering triangles exist,
C. R. Math. (Acad. Sci., Paris)
, 339 (2004), 365--370, PDF (168K)

A. Blokh, L. Oversteegen
Backward stability for polynomial maps with locally connected Julia sets
Trans. Amer. Math. Soc.
, 356 (2004), 119--133, PDF (227K)

A. Blokh, E. Teoh
How little is little enough?
Disc. and Cont. Dyn. Syst.
, 9 (2003), 969-978, PDF (212K)

A. Blokh
On Graph-Realizable Sets of Periods
J. Diff. Eq. Appl.
, 9 (2003), 343--357, PDF (246K)

A. Blokh, G. Levin
On dynamics of vertices of locally connected polynomial Julia sets
Proc. Amer. Math. Soc.
, 130 (2002), 30219-3230, PDF (222K)

A. Blokh, G. Levin
Growing trees, laminations and the dynamics on the Julia set
Ergodic Theory and Dynamical Systems
22 (2002), 63-97, PDF (399K)

A. Blokh, A. Fieldsteel
Sets that force recurrence
Proc. Amer. Math. Soc.
130 (2002), 3571-3578, PDF (303K)

A. Blokh, M. Misiurewicz
Attractors for graph critical rational maps
Trans. Amer. Math. Soc.
354 (2002), 3639-3661, PDF (300K)

A. Blokh, M. Misiurewicz
Rotation numbers for certain maps of an n-od
Topology and its Appl.
114 (2001), 27-48, PDF (202K)

A. Blokh, M. Misiurewicz
Typical limit sets of critical points for smooth interval maps
Ergodic Theory and Dynamical Systems
20 (2000), 15-45, PDF (333K)

A. Blokh, J. Mayer, L. Oversteegen
Recurrent critical points and typical limit sets for conformal measures
Topology and its Appl.
108 (2000), 233-244, PDF (203K)

A. Blokh
On the density of periodic orbits in limit sets with Hausdorff metric
Real Analysis Exchange 24 (1999), 503-521, PDF (245K)

A. Blokh, J. Mayer, L. Oversteegen
Recurrent critical points and typical limit sets of rational maps
Proc. Amer. Math. Soc.
127 (1999), 1215-1220, PDF (186K)

A. Blokh, M. Misiurewicz
Rotating an Interval and a Circle
Trans. Amer. Math. Soc.
351 (1999), 63-78, PDF (288K)

A. Blokh, M. Misiurewicz
Collet-Eckmann maps are Unstable
Comm. Math. Phys.
191(1998), 61-70, PDF (115K)

A. Blokh, M. Misiurewicz
Wild attractors of polymodal negative Schwarzian maps
Comm. Math. Phys.
199(1998), 397-416, PDF (154K)

A. Blokh, M. Misiurewicz
New Order for Periodic Orbits of Interval Maps
Ergodic Theory and Dynamical Systems
17(1997), 565-574, PDF (210K)

A. Blokh, M. Misiurewicz
Dense set of negative Schwarzian maps whose critical points have minimal limit sets
Discrete Contin. Dynam. Systems
4(1997), 141-158, PDF (267K)

A. Blokh, M. Misiurewicz
Entropy and Over-Rotation Numbers for Interval Maps
Mathematical Proceedings of Steklov Institute, dedicated to D. V. Anosov's 60th birthday, 216(1997), 229-235, PDF (182K)

A. Blokh, M. Misiurewicz
Entropy of Twist Interval Maps
Israel Journal of Mathematics
102(1997), 61-100, PDF (322K)

A. Blokh, A. Bruckner, P. Humke, J. Smital
The Space of limit Sets of a Continuous Map of the Interval
Trans. Amer. Math. Soc.
348 (1996), 1357-1372, PDF (404K)

A. Blokh, E. Coven
Sharkovskii Type of Cycles
Proc. Lond. Math. Soc.
28 (1996), 417-424, PDF(215K)

A. Blokh
Functional Rotation Numbers for One-Dimensional Maps
Trans. Amer. Math. Soc.
347 (1995), 499-514, PDF(479K)

A. Blokh
The Spectral Decomposition for One-Dimensional Maps
Dynamics Reported 4(1995), 1-59, PDF(432K)

A. Blokh
Rotation Numbers, Twists and a Sharkovskii-Misiurewicz-type Ordering for Patterns on the Interval
Ergodic Theory and Dynamical Systems
15(1995), 1--14, PDF(239K)

A. Blokh, E. Coven, L. Block
Zero Entropy Permutations
International Journal of Bifurcation and Chaos
5 (1995), 1331-1337, PDF(209K)

A. Blokh
Trees with Snowflakes and Zero Entropy Maps
Topology
, #2 33 (1994), 379-396, PDF(294K)

A. Blokh
On Rotation Intervals for Interval Maps
Nonlineraity
7 (1994), 1395-1417, PDF(310K)

A. Blokh
Periods Implying Almost All Periods for Tree Maps
Nonlineraity
5 (1992), 1375-1382, PDF(219K)

A. Blokh
The Set of All Iterates is Nowhere Dense in C([0,1],[0,1])
Trans. Amer. Math. Soc.
333 (1992), 787-798, PDF(384K)

A. Blokh, M. Lyubich
Measurable Dynamics of S-Unimodal Maps of the Interval
Ann. Sci. Ecole Norm. Sup. (4)
, #5, 24 (1991), 545-573, PDF(2.62M)

A.Blokh, E.Coven, M.Misiurewicz, Z.Nitecki
Roots of Continuous Piecewise Monotone Maps of an Interval
Acta Math. Univ. Comen. (Bratislava)
60 (1991), 3-10, PDF(294K)

A. Blokh
The Spectral Decomposition, Periods of Cycles and Misiurewicz Conjecture for Graph Maps
Lecture Notes in Math., Springer 1514 (1991), 24-31, PDF(204K)

A. Blokh, M. Lyubich
On Decomposition of One-Dimensional Dynamical Systems into Ergodic Components.
The Case of Negative Schwarzian

Leningr. Math. Jour., #1, 1 (1990), 137--155,

A. Blokh, M. Lyubich
Measure of Solenoidal Attractors of Unimodal Maps of the Segment
Math. Notes
, #5, 48 (1990), 1085-1090,

A. Blokh, M. Lyubich
Measure and Dimension of Solenoidal Attractors of One-Dimensional Dynamical Systems
Comm. Math. Phys.
127(1989), 573-583,

A. Blokh, M. Lyubich
Non-existence of Wandering Intervals and Structure of Topological Attractors of One - Dimensional Dynamical Systems.2 The Smooth Case
Ergodic Theory and Dynamical Systems
9 (1989), 751-758,

A. Blokh, M. Lyubich
On Typical Behavior of Trajectories of Transformations of the Interval
Theory of Functions, Functional Analysis and Applications, Kharkov 49 (1989), 5-15.

A. Blokh, M. Lyubich
Attractors of Maps of the Interval
Banach Center Publications (of the Semester on Dynamical Systems held in Warsaw) 23 (1989), 427--442.

A. Blokh, M. Lyubich
Ergodicity of transitive Unimodal Maps of the Interval
Ukrain. Journ. of Math.
41 (1989), 841-844.

A. Blokh, M. Lyubich
The Absence of Wandering Intervals in One-Dimensional Smooth Dynamical Systems
Soviet Mathematics-Doklady, #1, 39 (1989), pp. 169-172.

A. Blokh, M. Lyubich
Ergodic Properties of Transformations of the Interval
Functional Analysis and Applications
23 (1989), 48-49.

A. Blokh
On Dynamical Systems on One-Dimensional Branched Manifolds.3
Theory of Functions, Functional Analysis and Applications, Kharkov, 48 (1987), 32-46.

A. Blokh
On the Connection between Entropy and Transitivity for One-Dimensional Mappings
Russ. Math. Surv.
, #5, 42 (1987), 165-166.

A. Blokh, M. Lyubich
Attractors of Transformations of the Interval
Functional Analysis and Applications
21 (1987), 148-149.

A. Blokh
On Some Properties of Maps of the Interval with Constant Slope
Mathematical Physics and Functional Analysis, Kiev (1986), 127-136.

A. Blokh
On Dynamical Systems on One-Dimensional Branched Manifolds.1
Theory of Functions, Functional Analysis and Applications, Kharkov, 46 (1986), 8-18.

A. Blokh
On Dynamical Systems on One-Dimensional Branched Manifolds.2
Theory of Functions, Functional Analysis and Applications, Kharkov, 47 (1986), 67-77.

A. Blokh
On Transitive Maps of One-Dimensional Branched Manifolds
Differential - Difference Equations and Problems of Mathematical Physics, Kiev (1984), 3-9.

A. Blokh
Decomposition of Dynamical Systems on an Interval
Russ. Math. Surv.
, #5, 38 (1983), 133-134.

A. Blokh
On a Certain Interpretation of the Theorem of A.N.Sharkovskii
Oscillation and Stability of Solutions of Differential-Functional Equations, Kiev (1982), 3-8.

A. Blokh
On the Limit Behavior of One-Dimensional Dynamical Systems
Russ. Math. Surv.
, #1, 37(1982), 157-158.

A. Blokh
On Sensitive Mappings of the Interval
Russ. Math. Surv.
, #2, 37(1982), 203-204.

A. Blokh
On the spectral decomposition for piecewise-monotone maps of segment
Russ. Math. Surv.
, #3, 37(1982), 198-199.

Other publications

A. Blokh, M. Misiurewicz
Attractors and recurrence for dendrite-critical polynomials,
MPI
, Preprint 2004-96 in PDF (279K)

A. Blokh, M. Misiurewicz
Branched derivatives, ,
MPI
, Preprint 2004-42 in PS (336K)

A. Blokh, G. Levin
Growing trees, laminations and the dynamics on the Julia set
IHES Preprint IHES/M/99/77 (1999)

A. Blokh
Rotation Number for Unimodal Maps
MSRI (1994), Preprint #58-94.

A. Blokh, A. Bruckner, P. Humke, J. Smital
The Space of  omega-limit Sets of a Continuous Map of the Interval
MSRI (1994), Preprint #63-94.

A. Blokh, M. Misiurewicz
Entropy of Twist Interval Maps
MSRI (1994), Preprint #41-94.

A. Blokh
On Some Properties of Graph Maps: Spectral Decomposition, Misiurewicz Conjecture and Abstract Sets of Periods
Max-Planck-Institut fur Mathematik (1991), Preprint #35.

A. Blokh
Periods Implying Almost All Periods, Trees with Snowflakes, and Zero Entropy Maps
SUNY at Stony Brook (1991), Preprint #1991/13.

A. Blokh
The Spectral Decomposition for One-Dimensional Maps
SUNY at Stony Brook (1991), Preprint #1991/14.

A. Blokh
On the Limit Behavior of One-Dimensional Dynamical Systems.1
Moscow (1982), Preprint VINITI #1156-82.

A. Blokh
On Sensitive Mappings
Moscow (1982), Preprint VINITI #5676-82.

A. Blokh
On Some Entropy-like Invariants
Moscow (1982), Preprint VINITI #5677-82.


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