Related papers: Postcritical sets and saddle basic sets for Axiom …

In [ABM07], Abdulla et al. introduced the concept of decisiveness, an interesting tool for lifting good properties of finite Markov chains to denumerable ones. Later, this concept was extended to more general stochastic transition systems…

This paper constitutes a first attempt to do analysis with skew polynomials. Precisely, our main objective is to develop a theory of residues for skew rational functions (which are, by definition, the quotients of two skew polynomials). We…

We discuss the zero sets of two-variable polynomials as they relate to an approximation problem in the Hardy space on the bidisk.

In this article we aim to develop from first principles a theory of sum sets and partial sum sets, which are defined analogously to difference sets and partial difference sets. We obtain non-existence results and characterisations. In…

In this paper, we obtain new results on the critical points of a polynomial. We discuss the Sendov conjecture for polynomials of degree nine.

The critical relations for statistical properties on saddle-node bifurcations are shown to display undulating fine structure, in addition to their known smooth dependence on the control parameter. A piecewise linear map with the type-I…

Set theory is widely believed to provide a secure foundation for deductive mathematics, but current set theories do not quite do this. The mainstream essentially uses na\"\i ve set theory. After Russell's paradox showed this to be…

The field of analytic combinatorics is dedicated to the creation of effective techniques to study the large-scale behaviour of combinatorial objects. Although classical results in analytic combinatorics are mainly concerned with univariate…

Saddle point approximations, extremely important in a wide variety of physical contexts, require the analytical continuation of canonically conjugate quantities to complex variables in quantum mechanics. An important component of this…

In this paper we show that if $p$ is a polynomial which bifurcates then the product map $(z,w)\mapsto(p(z),q(w))$ can be approximated by polynomial skew products possessing special dynamical objets called blenders. Moreover, these objets…

In arXiv:0805.0157v5, the authors define a class of derived stacks, called "perfect stacks" and show that for this class the categories of quasi-coherent sheaves satisfy a categorical K\"unneth formula. Motivated to extend their results to…

We establish a conjectured result of Dummit, Granville and Kisilevsky for the maximum bias in P2 races, which compare the number of P2's $\leq x$ whose prime factors, evaluated at a given quadratic character, take specifc values.

In this work we present a computation paradigm based on a concurrent and incremental construction of proof nets (de-sequentialized or graphical proofs) of the pure multiplicative and additive fragment of Linear Logic, a resources conscious…

We study the yielding transition of a two dimensional amorphous system under shear by using a mesoscopic elasto-plastic model. The model combines a full (tensorial) description of the elastic interactions in the system, and the possibility…

Toward the understanding of bifurcation phenomena of dynamics on the Berkovich projective line $\mathbb{P}^{1,an}$ over non-archimedean fields, we study the stability (or passivity) of critical points of families of polynomials parametrized…

Methods for stochastic trace estimation often require the repeated evaluation of expressions of the form $z^T p_n(A)z$, where $A$ is a symmetric matrix and $p_n$ is a degree $n$ polynomial written in the standard or Chebyshev basis. We show…

Anzai skew-products are shown to be uniquely ergodic with respect to the fixed-point subalgebra if and only if there is a unique conditional expectation onto such a subalgebra which is invariant under the dynamics. For the particular case…

We propose a stochastic extension of the primal-dual hybrid gradient algorithm studied by Chambolle and Pock in 2011 to solve saddle point problems that are separable in the dual variable. The analysis is carried out for general…

The equivariant cohomology for actions of compact connected abelian groups and elementary abelian p-groups have been widely studied in the last decades. We study some of these results on actions of finite cyclic groups over a field of…

We investigate the effects of aperiodic interactions on the critical behavior of an interacting two-polymer model on hierarchical lattices (equivalent to the Migadal-Kadanoff approximation for the model on Bravais lattices), via…