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pro vyhledávání: '"Pakovich, Fedor"'
Autor:
Pakovich, Fedor
With each holomorphic map $f: R \rightarrow \mathbb C\mathbb P^1$ between compact Riemann surfaces one can associate a combinatorial datum consisting of the genus $g$ of $R$, the degree $n$ of $f$, the number $q$ of branching points of $f$, and the $
Externí odkaz:
http://arxiv.org/abs/2408.10874
Autor:
Orevkov, Stepan, Pakovich, Fedor
For a non-constant complex rational function $P$, the lemniscate of $P$ is defined as the set of points $z\in \mathbb C$ such that $\vert P(z)\vert =1$. The lemniscate of $P$ coincides with the set of real points of the algebraic curve given by the e
Externí odkaz:
http://arxiv.org/abs/2309.04983
The concepts of differentiation and integration for matrices are known. As far as each matrix is differentiable, it is not clear a priori whether a given matrix is integrable or not. Recently some progress was obtained for diagonalizable matrices, ho
Externí odkaz:
http://arxiv.org/abs/2303.13239
Autor:
Pakovich, Fedor
Let $k$ be an algebraically closed field of characteristic zero, and $k[[z]]$ the ring of formal power series over $k$. In this paper, we study equations in the semigroup $z^2k[[z]]$ with the semigroup operation being composition. We prove a number o
Externí odkaz:
http://arxiv.org/abs/2208.08365
Autor:
Pakovich, Fedor
Let $k$ be an algebraically closed field of characteristic zero, and $k[[z]]$ the ring of formal power series over $k$. We provide several characterizations of right amenable finitely generated subsemigroups of $z^2k[[z]]$ with the semigroup operatio
Externí odkaz:
http://arxiv.org/abs/2208.04640
Autor:
Pakovich, Fedor
We give lower bounds for genera of components of fiber products of holomorphic maps between compact Riemann surfaces, extending results on genera of components of algebraic curves of the form $A(x)-B(y)=0,$ where $A$ and $B$ are rational functions.
Externí odkaz:
http://arxiv.org/abs/2201.08231
Autor:
Pakovich, Fedor
We formulate some problems and conjectures about semigroups of rational functions under composition. The considered problems arise in different contexts, but most of them are united by a certain relationship to the concept of amenability.
Commen
Commen
Externí odkaz:
http://arxiv.org/abs/2110.01507
Autor:
Pakovich, Fedor
Let $F$ be a rational function of one complex variable of degree $m\geq 2$. The function $F$ is called simple if for every $z\in \mathbb C\mathbb P^1$ the preimage $F^{-1}\{z\}$ contains at least $m-1$ points. We show that if $F$ is a simple rational
Externí odkaz:
http://arxiv.org/abs/2107.05963
Autor:
Pakovich, Fedor
Let $A$ be a rational function of one complex variable, and $z_0$ its repelling fixed point with the multiplier $\lambda.$ Then a Poincar\'e function associated with $z_0$ is a function $\mathcal{P}_{A,z_0,\lambda}$ meromorphic on $\mathbb C$ such th
Externí odkaz:
http://arxiv.org/abs/2106.05770
Autor:
Pakovich, Fedor
Let $P_1,P_2,\dots, P_k$ be complex polynomials of degree at least two that are not simultaneously conjugate to monomials or to Chebyshev polynomials, and $S$ the semigroup under composition generated by $P_1,P_2,\dots, P_k$. We show that all element
Externí odkaz:
http://arxiv.org/abs/2009.12261