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


Teaching





Preprints

Semiconjugate rational functions: a dynamical approach. pdf

On generalized Lattès maps. pdf

Finiteness theorems for commuting and semiconjugate rational functions. pdf



Publications

On rational functions whose normalization has genus zero or one,
Acta. Arith., to appear. pdf

Davenport-Zannier  Polynomials over Q, (with. A. Zvonkine),
Int. J. Number Theory, to appear. pdf

Polynomial semiconjugacies, decompositions of iterations, and invariant curves,
Ann. Sc. Norm. Super. Pisa Cl. Sci., to appear. pdf

Recomposing rational functions,
Int.  Math. Res. Not., to appear. pdf

On algebraic curves A(x)-B(y)=0 of genus zero,
Math. Z., to appear. 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. ps

On polynomials orthogonal to all powers of a Chebyshev polynomial on a segment,
Israel J. Math., Vol. 142 (2004), 273—283. ps

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). ps

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). ps

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)