Related papers: Meromorphic first integrals of analytic diffeomorp…

In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…

We show that various functionals related to the supremum of a real function defined on an arbitrary set or a measure space are Hadamard directionally differentiable. We specifically consider the supremum norm, the supremum, the infimum, and…

The dynamically defined measure (DDM) $\Phi$ arising from a finite measure $\phi_0$ on an initial $\sigma$-algebra on a set and an invertible map acting on the latter is considered. Several lower bounds for it are obtained and sufficient…

In this paper we present a result about analytic functions f defined on the open unit disc and with a finite number of exceptional values containedin the real interval (0, 1). We find an upper bound for the modulus of f' in 0. This bound is…

We investigate the size of fixed point sets of automorphisms of bounded domains in $\mathbb{C}^n$. In one complex variable, a nontrivial automorphism has at most two fixed points, but in higher dimensions fixed point sets need not be…

We obtain sharp lower and upper bounds for the number of maximal (under inclusion) independent sets in trees with fixed number of vertices and diameter. All extremal trees are described up to isomorphism.

We consider discrete-time one-dimensional random dynamical systems with bounded noise, which generate an associated set-valued dynamical system. We provide necessary and sufficient conditions for a discontinuous bifurcation of a minimal…

In this article we have studied complex linear homogeneous difference equations where the coefficients are meromorphic functions, having finite iterated p-phi order. We have made some estimations on the growth of its nontrivial solutions.…

It is proved that the mean signature of multi-dimensional fractional brownian motion admits a meromorphic continuation in the hurst parameter to the entire complex plane. Each contstituent mean iterated integral is a sum of hypergeometric…

The aim of this paper is fourfold. Firstly, we introduce and study the f-ultra-harmonic maps. Secondly, we recall the geometric dynamics generated by a first order normal PDE system and we give original results regarding the geometric…

In this paper we prove a number of results concerning uniqueness of a meromorphic function as well as its derivative sharing one or two sets. In particular, we deal with the specific question raised in [18], [19], [20] and ultimately…

We propose a robust and computationally efficient algorithm to generically construct first return maps of dynamical systems from time series without the need for embedding. Typically, a first return map is constructed using a heuristic…

The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…

We prove a new bound on the number of shared values of distinct meromorphic functions on a compact Riemann surface, explain a mistake in a previous paper on this topic, and give a survey of related questions.

It is known that Iterated Function Systems generated by orientation preserving homeomorphisms of the unit interval admit a unique invariant measure on $(0,1)$. The setup for this result is the positivity of Lyapunov exponents at both fixed…

We describe a canonical procedure for associating to any (germ of) holomorphic self-map f of C^n fixing the origin such that df_O is invertible and non-diagonalizable an n-dimensional complex manifold M, a holomorphic map p from M to C^n, a…

We compute explicitly the automorphism and outer automorphism group of all large-type free-of-infinity Artin groups. Our strategy involves reconstructing the associated Deligne complexes in a purely algebraic manner, i.e. in a way that is…

We introduce and study algebraic dynamical systems generated by triangular systems of rational functions. We obtain several results about the degree growth and linear independence of iterates as well as about possible lengths of…

Let $f$ be a meromorphic function with bounded set of singular values and for which infinity is a logarithmic singularity. Then we show that $f$ has infinitely many repelling periodic points for any minimal period $n\geq1$, using a much…

Fewnomial theory began with explicit bounds -- solely in terms of the number of variables and monomial terms -- on the number of real roots of systems of polynomial equations. Here we take the next logical step of investigating the…