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
Refereed papers
A. Blokh, M. Misiurewicz
Local critical perturbations of unimodal
maps,
submitted , PDF (282K)
A. Blokh, L. Oversteegen
Wandering Gaps for Weakly Hyperbolic
Polynomials,
to appear, PDF (295K)
A. Blokh, L. Oversteegen
The Julia sets of basic uniCremer
polynomials of arbitrary degree,
submitted , PDF (282K)
A. Blokh, X. Buff, A. Cheritat, L. Oversteegen
The solar Julia
sets of basic quadratic Cremer polynomials,
submitted , PDF (357K)
A. Blokh, J. Bobok
Asymptotic behavior of the entropy of interval
maps,
to appear , PDF (200K)
A. Blokh, M. Misiurewics, L. Oversteegen
Sets of constant distance
from a compact set,
to appear , PDF
(178K)
A. Blokh, L. Oversteegen
Monotone images of Cremer Julia sets,
to appear , PDF (170K)
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, M. Misiurewicz
Branched derivatives,
Nonlinearity, 18 (2005), 703--715.
PDF (335K)
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
Necessary conditions for the existence of wandering vertices
for cubic laminations,
Disc. and Cont. Dyn. Syst.,
13 (2005), 13--34.
PDF (280K)
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, 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, 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, C. Cleveland, M. Misiurewicz
Julia sets of expanding polymodials,
Ergodic Theory and Dynamical Systems, 25 (2005), no. 5, 1691-1718
PS (567K)
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, L. Oversteegen, E. Tymchatyn
On minimal maps of
2-manifolds,
Ergodic Theory and Dynamical Systems, 25 (2005), #1,
41--57 PDF (220K)
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
Branched derivatives, ,
MPI Preprint 2004-42, submitted
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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