Fedor Pakovich
Email: pakovich at math dot bgu dot ac dot il
Preprints
Holomorphic maps sharing preimages over finitely generated fields, pdf
On interwined polynomials, pdf
Periodic curves for general endomorphisms of CP1×CP1. pdf
Rational functions sharing preimages and height functions. pdf
Hurwitz existence problem and fiber products. pdf
Publications
Algebraic functions with infinitely many values in a number field, to appear in J. Théor. Nombres Bordeaux, pdf
On dessins d'enfants with equal supports, J. Math. Sci. (N.Y.), on line first, pdf
Right amenability in semigroups of formal power series, Groups Geom. Dyn. 20 (2026), no. 1, 205–214. pdf
On symmetries of iterates of rational functions, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XXVI (2025), 1677-1701. pdf
Lower bounds for genera of fiber products, Israel. J. Math., 269 (2025), 475–500. pdf
On iterates of rational functions with maximal number of critical values, J. Anal. Math., 156 (2025), no. 1, 213–251. pdf
On intersection of lemniscates of rational functions (with Orevkov), Arnold Math. J., Vol. 11 , no. 1, 2025, 7–26. pdf
On algebraic dependencies between Poincaré functions, Ergodic Theory Dynam. Systems,, 45 (2025), no. 3, 915–935. pdf
Semigroups of rational functions: some problems and conjectures, Panor. Synthèses, 2024, 89–104. pdf
Functional equations in formal power series, Ann. Fen. Mat. 49 (2024), no. 2, 601-620. pdf
Integrability of matrices (with Danielyan, Guterman, and Kreines), Linear Algebra Appl. 684 (2024), 37-62. pdf
Tame rational functions: Decompositions of iterates and orbit intersections, J. Eur. Math. Soc., (JEMS) 25 (2023), no. 10, 3953-3978. pdf
Invariant curves for endomorphisms of P1×P1, Math. Ann. 385 (2023), no. 1-2, 259-307. pdf
On amenable semigroups of rational functions, Trans. Amer. Math. Soc. 375 (2022), no. 11, 7945-7979. pdf
Sharing a measure of maximal entropy in polynomial semigroups, Int. Math. Res. Not. IMRN 2022, no. 18, 13829-13840. 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, 387-396 (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