Related papers: Some counterexamples in dynamics of rational semig…
We investigate to what extent Fatou set, Julia set and escaping set of transcendental semigroup is respectively equal to the Fatou set, Julia set and escaping set of its subsemigroup. We define partial fundamental set and fundamental set of…
We give an estimate of the minimal positive value of the Wilf function of a numerical semigroup in terms of its concentration. We describe necessary conditions for a numerical semigroup to have negative Eliahou number in terms of its…
The aim of this work is to describe the equivalence relations in $\Q/\Z$ that arise as the rational lamination of polynomials with all cycles repelling. We also describe where in parameter space one can find a polynomial with all cycles…
We establish Bowen's formula for the Julia set of a non-elementary, expanding, irreducible and aperiodic rational graph-directed Markov system satisfying the backward separating condition. Towards this end, we shall prove that the…
Let G be a semigroup of rational functions of degree at least two where the semigroup operation is composition of functions. We prove that the largest open subset of the Riemann sphere on which the semigroup G is normal and is completely…
We show that a rational function $f$ of degree $>1$ on the projective line over an algebraically closed field that is complete with respect to a non-trivial and non-archimedean absolute value has no potentially good reductions if and only…
It is well-known that abelian varieties are projective, and so that there exist explicit polynomial and rational functions which define both the variety and its group law. It is however difficult to find any explicit polynomial and rational…
It is proved that, in certain subgroups of direct products of countable groups, the property of being an unconditionally closed set coincides with that of being an algebraic set. In particular, these properties coincide in all Abelian…
We classify the finite-dimensional rational representations $V$ of the exceptional algebraic groups $G$ with $\mathfrak g={\sf Lie}(G)$ such that the symmetric invariants of the semi-direct product $\mathfrak g\ltimes V$, where $V$ is an…
We develop a theory of quasisymmetries for finitely ramified fractals, with applications to finitely ramified Julia sets. We prove that certain finitely ramified fractals admit a naturally defined class of "undistorted metrics" that are all…
Rational maps on the Riemann sphere occupy a distinguished niche in the general theory of smooth dynamical systems. First, rational maps are complex-analytic, so a broad spectrum of techniques can contribute to their study (quasiconformal…
We adapt the abstract concepts of abelianness and centrality of universal algebra to the context of inverse semigroups. We characterize abelian and central congruences in terms of the corresponding congruence pairs. We relate centrality to…
In \cite{Ioana:vNsuperrigidity}, Ioana introduced three new invariants of type II$_1$ factors: the one-sided fundamental group, the endomorphism semigroup and the set of right-finite bimodules. In \cite{Ioana:vNsuperrigidity}, he does not…
Complex dynamics deals with the iteration of holomorphic functions. As is well- known, the first functions to be studied which gave non-trivial dynamics were quadratic polynomials, which produced beautiful computer generated pictures of…
We give a characterization of hypercyclic finitely generated abelian semigroups of matrices on C^n using the extended limit sets (the J-sets). Moreover we construct for any n\geq 2 an abelian semigroup G of GL(n;C) generated by n + 1…
Semiuniform semigroups provide a natural setting for the convolution of generalized finite measures on semigroups. A semiuniform semigroup is said to be ambitable if each uniformly bounded uniformly equicontinuous set of functions on the…
It is well known that results on zero-sum sequences over a finitely generated abelian group can be translated to statements on generators of rings of invariants of the dual group. Here the direction of the transfer of information between…
Non-classical negations may fail to be contradictory-forming operators in more than one way, and they often fail also to respect fundamental meta-logical properties such as the replacement property. Such drawbacks are witnessed by intricate…
A set $R\subset \mathbb{N}$ is called rational if it is well-approximable by finite unions of arithmetic progressions. Examples of rational sets include many classical sets of number-theoretical origin such as the set of squarefree numbers,…
A commutative semigroup of abstract factorials is defined in the context of the ring of integers. We study such factorials for their own sake, whether they are or are not connected to sets of integers. Given a subset X of the positive…