Fedor Pakovich
Professor
Department of Mathematics
Ben Gurion University of the Negev
P.O.B. 653 Beer Sheva
8410501 ISRAEL
Office: Deichman 310
Research interests: Complex analysis, Number Theory, Complex and Arithmetic Dynamics
Preprints
Tame rational functions: Decompositions of iterates and orbit intersections. pdf
Invariant curves for endomorphisms of P^1×P^1.
pdf
Finiteness theorems for commuting and semiconjugate
rational functions. pdf
Publications
On rational functions sharing the measure of maximal entropy,
Arnold Math. J., accepted. pdf
Davenport - Zannier Polynomials and
Weighted Trees (book) (with N. Adrianov and A. Zvonkin), Mathematical Surveys and Monographs series
of the AMS, to appear. pdf
Commuting rational functions revisited, Ergodic Theory Dynam. Systems, accepted. pdf
On generalized Lattès maps,
J. Anal. Math., accepted. pdf
Level curves of rational functions and unimodular
points on rational curves, (with I. Shparlinski), Proc.
Amer. Math. Soc. 148 (2020), 1829-1833. pdf
Algebraic curves Aol(x)-U(y)=0 and arithmetic of orbits of rational
functions, Mosc. Math. J., Vol. 20 (2020), no 1,
153-183. pdf
On mutually semiconjugate rational
functions, Arnold Math. J., (2019) 5:339-354. pdf
Recomposing rational functions, Int. Math. Res. Not., 2019, no. 7, 1921-1935. pdf
Semiconjugate
rational functions: a dynamical approach, Arnold Math. J., 4 (2018), no. 1,
59–68. pdf
On rational functions whose normalization has genus zero or
one,
Acta. Arith., 182 (2018) , 73-100. pdf
On algebraic curves A(x)-B(y)=0 of
genus zero,
Math. Z., Vol. 288, Issue 1, (2018), 299-310. pdf
Davenport-Zannier
Polynomials over Q, (with. A.
Zvonkine),
Int. J. Number Theory, 14 (2018), no. 4, 925-974. pdf
Polynomial semiconjugacies, decompositions of iterations, and
invariant curves,
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), Vol. XVII (2017), 1417-1446. pdf
Solution of the parametric Center Problem for Abel Equation,
J. Eur. Math. Soc., 19 (2017), no. 8, 2343-2369. pdf
On decompositions of trigonometric polynomials,
Israel J. Math., 217 (2017), 337-353. pdf
On semiconjugate rational
functions,
Geom. Funct. Anal., 26 (2016), 1217-1243. pdf
Algebraic Geometry of the Center-Focus problem for Abel
Differential Equation,
(with Y. Yomdin, M. Briskin),
Ergodic Theory and Dynam. Sys.,Volume 36, Issue 3, (2016) 714–744. pdf
Parametric Center-Focus Problem for Abel Equation, (with Y. Yomdin, M. Briskin),
Qual. Theory Dyn. Syst., , (2014)
13:289-303. pdf
Weak and strong composition conditions for the Abel
differential equation,
Bull. Sci. Math., 138 (2014), 993-998. pdf
Minimum Degree of the Difference of Two Polynomials over Q
and Weighted Plane Trees,
(with. A. Zvonkine),
Selecta Math., 20, no. 4 (2014), 1003-1065. pdf
Moments on Riemann surfaces and hyperelliptic
Abelian integrals,
(with L. Gavrilov),
Comm. Math. Helvetici, 89, No 1, (2014) pp. 125–155. pdf
On rational functions orthogonal to all powers of a given
rational function on a curve,
Moscow Math. Journal, Volume 13, Issue 4, (2013) 693–731.
pdf
Generalized "second Ritt
theorem" and explicit solution of the polynomial moment problem,
Compositio Math. 149 (2013), 705-728. pdf
Algebraic curves P(x)-Q(y)=0 and
functional equations,
Complex Var. and Elliptic Equ., 56 (2011), no. 1-4,
199–213. pdf
Moment Vanishing Problem and Positivity: Some Examples
(with J. P. Francoise, Y. Yomdin, W. Zhao),
Bull. Sci. Math., 135 (2011), no. 1, 10-32. pdf
Jordan-Holder theorem for imprimitivity
systems and maximal decompositions of rational functions
(with M. Muzychuk),
Proc. Lond. Math. Soc., 102 (2011)
, no. 1, 1-24. pdf
Laurent polynomial moment problem: a case study
(with A. Zvonkin and C. Pech),
Contemp. Math., 532 (2010), 177-194. pdf
On the equation P(f)=Q(g), where P,Q
are polynomials and f,g are entire functions,
Amer. Journal of Math., 132 (2010), no. 6, 1591-1607. pdf
Prime and composite Laurent polynomials,
Bull. Sci. Math., 133 (2009), 693-732. pdf
Solution of the polynomial moment problem
(with M. Muzychuk).
Proc. Lond. Math. Soc., 99 no. 3, 633–657 (2009). pdf
Solution of the Hurwitz problem for Laurent polynomials,
J. Knot Theory Ramifications, 18, No. 2, 271-302 (2009). pdf
On trees covering chains or stars,
J. Math. Sci., New York, 158, No. 1, 148-154 (2009). pdf
Arithmetics
of conservative polynomials and yet another action of the group Gal(Q/Q) on plane trees,
J. Théor. Nombres
Bordeaux, 20, 205-218 (2008). pdf
On analogues of the theorems for rational functions with at
most two poles,
Russ. Math. Surv. 63, No. 2, 386-387 (2008). pdf
On polynomials sharing preimages of compact sets, and related questions,
Geom. Funct. Anal, 18,
No. 1, 163-183 (2008). pdf
On the functional equation F(A(z))=G(B(z)),
where A,B are polynomial and F,G are continuous functions,
Math. Proc. Cam. Phil. Soc., 143, No. 2, 469-472
(2007), pdf
Remark on the Chebotarev theorem
about roots of unity,
Integers 7 (2007), A18 (electronic). pdf
On polynomials orthogonal to all powers of a
given polynomial on a segment,
Bull. Sci. Math. 129 (2005), 749-774. pdf
Cauchy type integrals of Algebraic functions
(with N. Roytvarf and Y. Yomdin),
Israel J. Math., Vol. 144 (2004), 221-291. pdf
On polynomials orthogonal to all powers of a Chebyshev
polynomial on a segment,
Israel J. Math., Vol. 142 (2004), 273—283. pdf
Polynomial moment problem,
Addendum to the paper by Y. Yomdin,
Mosc. Math. J., 3(2003), no. 3, 1167-1195. pdf
On the
polynomial moment problem,
Math. Res. Lett., 10, no. 2-3, 401--410 (2003). pdf
A counterexample to the ``composition conjecture'',
Proc. Amer. Math. Soc. 130, 3747-3749 (2002). pdf
On trees admitting morphisms onto hedgehogs or onto chains,
Russ. Math. Surv. 55, No.3,
593-594 (2000).
Combinatoire
des arbres planaires et arithmetique des courbes hyperelliptiques,
Ann. Inst. Fourier 48, No.2, 323-351 (1998). pdf
A remark on complex polynomials of least deviation
(with I. V. Ostrovskii and M. G. Zaidenberg),
Int. Math. Res. Not. 1996, No.14, 699-703 (1996). pdf
Sur un probleme d'unicite
pour les functions meromorphes,
C. R. Acad. Sci., Paris (Ser. I) 323, No.7, 745-748 (1996). ps
Elliptics polynomials,
Russ. Math. Surv. 50, No.6, 1292-1294 (1995).
Locally nilpotent derivations of polynomial rings,
Math. Notes 58, No.2, 890-891 (1995)