Fedor Pakovich
Email: pakovich at math dot bgu dot ac dot il
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
Lower bounds for genera of fiber products. pdf
Semigroups
of rational functions: some problems and conjectures. pdf
On iterates of rational
functions with maximal number of critical values. pdf
On algebraic dependencies
between Poincaré functions. pdf
On symmetries of iterates of
rational functions. pdf
Publications
On amenable semigroups of
rational functions, Trans. Amer.
Math. Soc., accepted. pdf
Tame rational functions:
Decompositions of iterates and orbit intersections, J. Eur.
Math. Soc., accepted. pdf
Invariant curves for
endomorphisms of P^1×P^1, Math. Ann., https://doi.org/10.1007/s00208-021-02304-5. pdf
Sharing a measure of
maximal entropy in polynomial semigroups, Int. Math. Res. Not., doi:10.1093/imrn/rnab076.
pdf
Commuting
rational functions revisited, Ergodic Theory Dynam.
Systems, 41
(2021), no. 1, 295 - 320, pdf
On
generalized Lattès maps, J. Anal. Math., 142
(2020), no. 1, 1–39. pdf
On rational functions sharing
the measure of maximal entropy, Arnold Math. J., 6, –396 (2020), pdf
Finiteness
theorems for commuting and semiconjugate rational
functions, Conform. Geom. Dyn., 24 (2020),
202-229, pdf
Level curves
of rational functions and unimodular points on rational curves, (with I. Shparlinski), Proc. Amer. Math. Soc. 148
(2020), 1829-1833. pdf
Davenport - Zannier Polynomials and Weighted Trees (book) (with N. Adrianov and A. Zvonkin), Mathematical Surveys and Monographs
249, American Mathematical Society, Providence, 2020. 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). pdf
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). pdf
Elliptics polynomials,
Russ. Math. Surv. 50, No.6, 1292-1294 (1995). pdf
Locally
nilpotent derivations of polynomial rings,
Math. Notes 58, No.2, 890-891 (1995). pdf