Related papers: Non-Martingale Fixed-Point Processes for Iterated …

Conditions are given which imply that certain non-autonomous analytic iterated function systems (NIFS's) in the complex plane have uniformly perfect attractor sets, while other conditions imply the attractor is pointwise thin, and thus…

We exhibit invariants of smooth projective algebraic varieties with integer values, whose nonvanishing modulo p prevents the existence of an action without fixed points of certain finite p-groups. The case of base fields of characteristic p…

Using graph-theoretic techniques for f.g. subgroups of $F^{\mathbb{Z}[t]}$ we provide a criterion for a f.g. subgroup of a f.g. fully residually free group to be of finite index. Moreover, we show that this criterion can be checked…

We study the question of finite generation of saturated multi-Rees algebras and investigate the asymptotic behaviour of related length functions. In the setup of excellent local domains, we show that the saturated multi-Rees algebra of a…

We study a stochastically perturbed version of the well-known Krasnoselski--Mann iteration for computing fixed points of nonexpansive maps in finite dimensional normed spaces. We discuss sufficient conditions on the stochastic noise and…

Any maximal monotone operator can be characterized by a convex function. The family of such convex functions is invariant under a transformation connected with the Fenchel-Legendre conjugation. We prove that there exist a convex…

We consider the vector space $E_{\rho,p}$ of entire functions of finite order, whose types are not more than $p>0$, endowed with Frechet topology, which is generated by a sequence of weighted norms. We call a function $f\in E_{\rho,p}$ {\it…

We study fundamental groups of non compact Riemannian manifolds. We find conditions which ensure that the fundamental group is trivial, finite or finitely generated.

Using an adelic approach we simultaneously consider real and p-adic aspects of dynamical systems whose states are mapped by linear fractional transformations isomorphic to some subgroups of GL (2, Q), SL (2, Q) and SL (2, Z) groups. In…

Let $f(x) \in K(x)$ be a quadratic polynomial where $K$ is a field of characteristic not equal to $2$. The associated arboreal Galois representation of the absolute Galois group of $K$ acts on a regular rooted binary tree. Boston and Jones…

Let $K$ be a finitely generated field of characteristic zero. We study, for fixed $m \geq 2$, the rational functions $\phi$ defined over $K$ that have a $K$-orbit containing infinitely many distinct $m$th powers. For $m \geq 5$ we show the…

We study the class of Az\'ema-Yor processes defined from a general semimartingale with a continuous running maximum process. We show that they arise as unique strong solutions of the Bachelier stochastic differential equation which we prove…

We consider expansive group actions on a compact metric space containing a special fixed point denoted by $0$, and endomorphisms of such systems whose forward trajectories are attracted toward $0$. Such endomorphisms are called…

The aim of this paper is to establish some results regarding Infinite Iterated Function Systems with the help of the Tarski-Kantorovitch fixed-point principles for maps on partially ordered sets. To this end we introduce two new classes of…

A fixed point theorem is proved for inverse transducers, leading to an automata-theoretic proof of the fixed point subgroup of an endomorphism of a finitely generated virtually free group being finitely generated. If the endomorphism is…

We study in detail the profinite group G arising as geometric \'etale iterated monodromy group of an arbitrary quadratic polynomial over a field of characteristic different from two. This is a self-similar closed subgroup of the group of…

We prove that the arboreal Galois representation attached to a large class of quadratic polynomials defined over a field of rational functions in characteristic zero has finite index in the full automorphism group of the associated preimage…

For a real valued function, a point is critical if its derivatives are zero, and a critical point is a saddle point if it is not a local extrema. In this paper, we study algorithms to find saddle points of general Morse index. Our approach…

Finite determinacy for mappings has been classically thoroughly studied in numerous scenarios in the real- and complex-analytic category and in the differentiable case. It means that the map-germ is determined, up to a given equivalence…

Let $K$ be a function field of characteristic $p\geq0$ or a number field over which the $abc$ conjecture holds, and let $\phi(x)=x^d+c \in K[x]$ be a unicritical polynomial of degree $d\geq2$ with $d \not\equiv 0,1\pmod{p}$. We completely…