Alexander Blokh
Department of Mathematics
University of Alabama at Birmingham
Birmingham, Alabama 35294
Fax: (205) 934-9025
Telephone: (205) 934-2154
PUBLICATIONS
(See
reviews in Mathematical Reviews)
Refereed papers
A. Blokh, G. Levin, L. Oversteegen, V. Timorin
Maps with no a priori bounds,
Commnications in Mathematical Physics ,
406 (2025), issue 6, article number 141,
15 pages, 2 figures, paper in PDF (1,056K)
A. Blokh, L. Oversteegen, V. Timorin, Y. Wang
A model of the cubic connectedness locus,
38 (2025), Number 7, 32 pages, 1 figure, paper in PDF
A. Blokh, L. Oversteegen, N. Selinger, V. Timorin, S. Vejandla
Lavaurs algorithm for cubic symmetric polynomials,
33 pages, 8 figures, published online on January 6, 2025 in
Ergodic Theory and Dynamical Systems , paper in PDF (2,311K)
A. Blokh, M. Misiurewicz
Evolution of the Sharkovsky Theorem,
Ukrainian Mathematical Journal 76 (2024), 48-61,
paper in PDF (326K)
A. Blokh, L. Oversteegen, V. Timorin
Upper bounds for the moduli of polynomial-like maps,
24 pages, 3 figures, Paper No. 035003 published online in Nonlinearity ,
37 (2024), paper in PDF (729K)
A. Blokh, L. Oversteegen, N. Selinger, V. Timorin, S. Vejandla
Symmetric Cubic Laminations,
Conformal geometry and dynamics 27 (2023), 264-293,
paper in PDF (2,239K)
A. Blokh, L. Oversteegen, V. Timorin
Immediate renormalization of cubic complex
polynomials with empty rational lamination,
Moscow Mathematical Journal,
23 (2023), 441-461,
paper in PDF (697K)
A. Blokh, P. Haissinsky, L. Oversteegen, V. Timorin
On critical renormalization of complex polynomials,
28 pages, 3 figures, Paper No. 109135 published online in
Advances in Mathemaics ,
428 (2023), paper in PDF (589K)
A. Blokh, L. Oversteegen, V. Timorin
Slices of the Parameter Space of Cubic Polynomials,
Trans. Amer. Math. Soc. , 375 (2022) Number 8, 5313-5359
paper in PDF (1,900K)
A. Blokh, L. Oversteegen, A. Shepelevtseva, V. Timorin
Modeling core parts of Zakeri slices I,
Moscow Mathematical Journal,
22 (2022), No. 2, 1-31,
paper in PDF (2,253K)
S. Bhattacharya, A. Blokh, D. Schleicher
Unicritical Laminations,
Fundamenta Mathematicae,
258 (2022), 25-63,
paper in PDF (680K)
A. Blokh, L. Oversteegen, V. Timorin
Cutpoints of invariant subcontinua of polynomial Julia sets,
Arnold Mathematical Journal ,
8 (2022), 271-284, paper in PDF (344K)
S. Bhattacharya, A. Blokh
Monotonicity of the over-rotation interval for bimodal maps,
17 pages, 9 figures, Paper No. 108004 published online in
Topology and its Applications,
308 (2022), paper in PDF (491K)
A. Blokh, L. Oversteegen, N. Selinger, V. Timorin, S. Vejandla
Cubic symmetric polynomials,
34 pages, 3 figures, submitted (2023), paper in PDF (612K)
A. Blokh, A. Cheritat, L. Oversteegen, V. Timorin
Location of Siegel capture polynomials in parameter spaces
Nonlinearity , 34 (2021), 2430-2453,
paper in PDF (442K)
A. Blokh, L. Oversteegen, R. Ptacek, V. Timorin
Laminational models for some spaces of polynomials
of arbitrary degree,
Memoirs of the AMS , 265 (2020), No. 1288, paper in PDF (636K)
S. Bhattacharya, A. Blokh
Very badly ordered cycles of interval maps
Journal of Difference Equations and Applications , 26 (2020), 1067-1084,
paper in PDF (451K)
S. Bhattacharya, A. Blokh
Over-rotation intervals of bimodal interval maps
Journal of Difference Equations and Applications , 26 (2020), 1085-1113,
paper in PDF (699K)
A. Blokh, L. Oversteegen, V. Timorin
Dynamical generation
of parameter laminations,
Contemporary Mathematics
, 744 (2020), 205-229,
paper in PDF (587K)
A. Blokh, M. Misiurewicz
Renormalization towers and their
forcing,
Trans. Amer. Math. Soc. , 372 (2019), 8933�8953, paper in PDF (291K)
A. Blokh, M. Misiurewicz
Forcing among patterns with no
block structure,
Topology Proceedings, 54 (2019), 125-137, paper in PDF (223K)
A. Blokh, L. Oversteegen, R. Ptacek, V. Timorin
Models for spaces of dendritic polynomials,
Trans.
Amer. Math. Soc. , 372 (2019), 4829-4849,
paper in PDF (172K)
A. Blokh, L. Oversteegen, V. Timorin
Perfect subspaces of
quadratic laminations,
Science China Mathematics, 61 (2018), 2121-2138, paper in
PDF (1,260K)
A. Blokh, L. Oversteegen, R. Ptacek, V. Timorin
Complementary components to the cubic principal domain,
Proc. Amer. Math. Soc. , 146 (2018), 4649-4660, paper in
PDF (133K)
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
The
parameter space of cubic laminations with a fixed critical leaf,
Ergodic Theory and Dynamical Systems, 37 (2017),
2453�2486, paper in PDF
(392K)
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
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, 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
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
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, 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
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, PDF (341K)
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
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
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
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
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
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(1990), 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,
PDF(382K)
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
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.
