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

Algebraic functions with infinitely many values in a number field. pdf

Hurwitz existence problem and fiber products. pdf

 

Publications

Right amenability in semigroups of formal power series. to appear in Groups Geom. Dyn.  pdf

On symmetries of iterates of rational functions, to appear in Ann. Sc. Norm. Super. Pisa. pdf

On dessins d'enfants with equal supports, to appear in J. Math. Sci. (N.Y.) 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