Related papers: Critical curves of a piecewise linear map

We analyze a one-dimensional piecewise continuous discrete model proposed originally in studies on population ecology. The map is composed of a linear part and a power-law decreasing piece, and has three parameters. The system presents both…

This paper addresses the problem of determining the symmetries of a plane or space curve defined by a rational parametrization. We provide effective methods to compute the involution and rotation symmetries for the planar case. As for space…

We study the dynamics of a two-planet system, which evolves being in a $1/1$ mean motion resonance (co-orbital motion) with non-zero mutual inclination. In particular, we examine the existence of bifurcations of periodic orbits from the…

The main purpose of this paper is to define dynamical degrees for rational maps over an algebraic closed field of characteristic zero and prove some basic properties (such as log-concavity) and give some applications. We also define…

We introduce the class of rational plane curves parameterizable by conics as an extension of the family of curves parameterizable by lines (also known as monoid curves). We show that they are the image of monoid curves via suitable…

The abstract boundary uses sets of curves with the bounded parameter property (b.p.p.) to classify the elements of the abstract boundary into regular points, singular points, points at infinity and so on. To study how the classification…

Boundary labeling is a well-known method for displaying short textual labels for a set of point features in a figure alongside the boundary of that figure. Labels and their corresponding points are connected via crossing-free leaders. We…

We consider a modified notion of planarity, in which two nations of a map are considered adjacent when they share any point of their boundaries (not necessarily an edge, as planarity requires). Such adjacencies define a map graph. We give…

We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…

For planar polynomials systems the existence of an invariant algebraic curve limits the number of limit cycles not contained in this curve. We present a general approach to prove non existence of periodic orbits not contained in this given…

Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…

Symbolic dynamics, which partitions an infinite number of finite-length trajectories into a finite number of trajectory sets, describes the dynamics of a system in a simplified and coarse-grained way with a limited number of symbols. The…

In critical loop models, we define diagonal boundaries as boundaries that couple to diagonal fields only. Using analytic bootstrap methods, we show that diagonal boundaries are characterised by one complex parameter, analogous to the…

We consider a certain linear recursive relation with integer parameters and study some of its algebraic and geometric properties, with the purpose of estimating the number of chains of valences in the Farey series.

We present a novel algorithm for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. The motivation comes from the problem of establishing a…

Temporal graphs provide a useful model for many real-world networks. Unfortunately the majority of algorithmic problems we might consider on such graphs are intractable. There has been recent progress in defining structural parameters which…

We prove that almost every non-regular real quadratic map is Collet-Eckmann and has polynomial recurrence of the critical orbit (proving a conjecture by Sinai). It follows that typical quadratic maps have excellent ergodic properties, as…

This paper characterizes the values of partial regression coefficients, defined as projection coefficients onto the space spanned by explanatory variables, for random variables generated by linear structural equation models using graphical…

We compute the Euler characteristic of the moduli space of quadratic rational maps with a periodic marked critical point of a given period.

Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…