Related papers: Perturbations of graphs for Newton maps

This paper establishes limit theorems and quantitative statistical stability for a class of piecewise partially hyperbolic maps that are not necessarily continuous nor locally invertible. By employing a flexible functional-analytic…

The distortion of six different intrinsic metrics and quasi-metrics under conformal and quasiregular mappings is studied in a few simple domains $G\subsetneq\mathbb{R}^n$. The already known inequalities between the hyperbolic metric and…

Let $H^d$ be the set of all rational maps of degree $d\ge 2$ on the Riemann sphere which are expanding on Julia set. We prove that if $f\in H^d$ and all or all but one critical points (or values) are in the immediate basin of attraction to…

We show that a nontrivial graph isomorphism problem of two undirected graphs, and more generally, the permutation similarity of two given $n\times n$ matrices, is equivalent to equalities of volumes of the induced three convex bounded…

We study a class of degenerate hyperbolic equations in a bounded domain whose degeneracy occurs at a boundary point. We first develop the weighted functional framework, prove well-posedness of the degenerate problem, and establish…

In this paper we analyze chaotic dynamics for two dimensional nonautonomous maps through the use of a nonautonomous version of the Conley-Moser conditions given previously. With this approach we are able to give a precise definition of what…

Dynamics on parabolic immediate basins for rational Newton maps of entire functions have been studied. It is proved that every parabolic immediate basin contains invariant accesses to the parabolic fixed point at infinity. Moreover, among…

We present four models for a random graph and show that, in each case, the probability that a graph is intrinsically knotted goes to one as the number of vertices increases. We also argue that, for $k \geq 18$, most graphs of order $k$ are…

We prove that a wide range of coloring problems in graphs on surfaces can be resolved by inspecting a finite number of configurations.

In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which…

In this paper we construct spanning trees in hyperbolic graphs that represent their hyperbolic compactification in a good way: so that the tree has a bounded number of distinct rays to each boundary point. The bound depends only on the…

Given a locally finite simple graph so that its degree is not bounded, every self-adjoint realization of the adjacency matrix is unbounded from above. In this note we give an optimal condition to ensure it is also unbounded from below. We…

We investigate a class of area preserving non-uniformly hyperbolic maps of the two torus. First we establish some results on the regularity of the invariant foliations, then we use this knowledge to estimate the rate of mixing.

We study large uniform random maps with one face whose genus grows linearly with the number of edges. They can be seen as a model of discrete hyperbolic geometry. In the past, several of these hyperbolic geometric features have been…

The Newton-Raphson basins of convergence, related to the equilibrium points, in the Sitnikov four-body problem with non-spherical primaries are numerically investigated. We monitor the parametric evolution of the positions of the roots, as…

We give a combinatorial upper bound for the gonality of a curve that is defined by a bivariate Laurent polynomial with given Newton polygon. We conjecture that this bound is generically attained, and provide proofs in a considerable number…

In this paper we investigate the perturbation properties of rational Misiurewicz maps, when the Julia set is the whole sphere (the other case is treated in [1]). In particular, we show that if f is a Misiurewicz map and not a flexible…

We consider the problem of partitioning a graph into a non-fixed number of non-overlapping subgraphs of maximum density. The density of a partition is the sum of the densities of the subgraphs, where the density of a subgraph is its average…

We study a class of degenerate parabolic equations with boundary point degeneracy in dimensions N>=2 and investigate the associated boundary observability problem by means of shape design. While one-dimensional degenerate models have been…

Inspired by [6, 7], we study the boundary regularity of constant curvature hypersurfaces in the hyperbolic space $\mathbb{H}^{n+1}$, which have prescribed asymptotic boundary at infinity. Through constructing the boundary expansions of the…