Related papers: A non-Borel special alpha-limit set in the square

We prove some properties of analytic multiplicative and sub-multiplicative cocycles. The results allow to construct natural invariant analytic sets associated to complex dynamical systems.

We establish the Borel computability of various C$^*$-algebra invariants, including the Elliott invariant and the Cuntz semigroup. As applications we deduce that AF algebras are classifiable by countable structures, and that a conjecture of…

Let $f: M \to M$ be a $C^{1+\alpha}$ map/diffeomorphism of a compact Riemannian manifold $M$ and $\mu$ be an expanding/hyperbolic ergodic $f$-invariant Borel probability measure on $M$. Assume $f$ is average conformal expanding/hyperbolic…

In this paper we address the question: How many pairwise non-isomorphic extremely amenable groups are there which are separable metrizable or even Polish? We show that there are continuum many such groups. In fact we construct continuum…

We introduce a new invariant of Borel reducibility, namely the notion of thickness; this associates to every sentence $\Phi$ of $\mathcal{L}_{\omega_1 \omega}$ and to every cardinal $\lambda$, the thickness $\tau(\Phi, \lambda)$ of $\Phi$…

It is now a classical result that an algebraic space locally of finite type over $\mathbf{C}$ is analytifiable if and only if it is locally separated. In this paper we study non-archimedean analytifications of algebraic spaces. We construct…

A toral algebraic set $A$ is an algebraic set in $\C^n$ whose intersection with $\T^n$ is sufficiently large to determine the holomorphic functions on $A$. We develop the theory of these sets, and give a number of applications to function…

In this article we treat a notion of continuity for a multi-valued function $F$ and we compute the descriptive set-theoretic complexity of the set of all $x$ for which $F$ is continuous at $x$. We give conditions under which the latter set…

Let $ E $ be a non-empty compact subset of the Riemann sphere and $T$ be a rational map of degree at least two. We study the associated \emph{orbital set}, that is, the backwards orbit of $E$ under $T$, and study the relationship between…

This paper, being the sequel of [An inverse problem in Polya-Schur theory. I. Non-genegerate and degenerate operators], studies a class of linear ordinary differential operators with polynomial coefficients called \emph{exactly solvable};…

This paper concerns $\mu$-limit sets of cellular automata: sets of configurations made of words whose probability to appear does not vanish with time, starting from an initial $\mu$-random configuration. More precisely, we investigate the…

The study of essential and strongly essential variables in functions defined on finite sets is a part of $k$-valued logic. We extend the main definitions from functions to terms. This allows us to apply concepts and results of Universal…

We show that, for every finitely generated group with decidable word problem and undecidable domino problem, there exists a sequence of effective subshifts whose inverse limit is not the topological factor of any effective dynamical system.…

The analytic and formal solutions to a family of singularly perturbed partial differential equations in the complex domain involving two complex time variables are considered. The analytic continuation properties of the solution of an…

We consider a family of dynamical systems (A,alpha,L) in which alpha is an endomorphism of a C*-algebra A and L is a transfer operator for \alpha. We extend Exel's construction of a crossed product to cover non-unital algebras A, and show…

We study from the perspective of Borel complexity theory the classification problem for multiplier algebras associated with operator algebraic varieties. These algebras are precisely the multiplier algebras of irreducible complete…

We prove that no quantifier-free formula in the language of group theory can define the $\aleph_1$-half graph in a Polish group, thus generalising some results from [6]. We then pose some questions on the space of groups of automorphisms of…

We revisit Akbulut and King's first example of a compact semialgebraic set which satisfies Sullivan's local Euler characteristic condition, but which is not homeomorphic to an algebraic set. A nontrivial obstruction is computed using the…

We prove in this paper that there exists some infinitary rational relations which are Sigma^0_3-complete Borel sets and some others which are Pi^0_3-complete. This implies that there exists some infinitary rational relations which are…

A Misiurewicz parameter is a complex number $c$ for which the orbit of the critical point $z=0$ under $z^2+c$ is strictly preperiodic. Such parameters play the same role as special points in dynamical moduli spaces that singular moduli…