Related papers: Combinatorics and topology of straightening maps I…

This paper introduces a class of polynomial maps in Euclidean spaces, investigates the conditions under which there exist Smale horseshoes and uniformly hyperbolic invariant sets, studies the chaotic dynamical behavior and strange…

A set of graphs are called cospectral if their adjacency matrices have the same characteristic polynomial. In this paper we introduce a simple method for constructing infinite families of cospectral regular graphs. The construction is valid…

For a compact $(2n+1)$-dimensional smooth manifold, let $\mu_M : B Diff_\partial (D^{2n+1}) \to B Diff (M)$ be the map that is defined by extending diffeomorphisms on an embedded disc by the identity. By a classical result of Farrell and…

For the family of complex rational functions of the form $R_{n,c,a}(z) = z^n + \dfrac{a}{z^n}+c$, known as ``Generalized McMullen maps'', for $a\neq 0$ and $n \geq 3$ fixed, we study the boundedness locus in some one-dimensional slices of…

The degree of a map between orientable manifolds is a fundamental concept in topology, providing deep insights into the structure of manifolds and the behavior of maps between them. Recently, this notion has been extensively studied,…

The parallel product of two rooted maps was introduced by S. E. Wilson in 1994. The main question of this paper is whether for a given reflexible map $M$ one can decompose the map into a parallel product of two reflexible maps. This can be…

The deautonomisation of birational maps that have the singularity confinement property, i.e. the construction of nonautonomous versions of such maps that preserve the singularity properties of the original, has proven crucial in our…

Quasiconformal maps are homeomorphisms with useful local distortion inequalities; infinitesimally, they map balls to ellipsoids with bounded eccentricity. This leads to a number of useful regularity properties, including quantitative…

Motivated by quantum thermodynamics we first investigate the notion of strict positivity, that is, linear maps which map positive definite states to something positive definite again. We show that strict positivity is decided by the action…

For non-negative integers $(d_n(k))_{k \ge 1}$ such that $\sum_{k \ge 1} d_n(k) = n$, we sample a bipartite planar map with $n$ faces uniformly at random amongst those which have $d_n(k)$ faces of degree $2k$ for every $k \ge 1$ and we…

In the early 60's J. B. Keller and D. Levy discovered a fundamental property: the instability tongues in Mathieu-type equations lose sharpness with the addition of higher-frequency harmonics in the Mathieu potentials. 20 years later V.…

Let $Rat_d$ denote the space of holomorphic self-maps of ${\bf P}^1$ of degree $d\geq 2$, and $\mu_f$ the measure of maximal entropy for $f\in Rat_d$. The map of measures $f\mapsto\mu_f$ is known to be continuous on $Rat_d$, and it is shown…

An oriented compact closed manifold is called inflexible if the set of mapping degrees ranging over all continuous self-maps is finite. Inflexible manifolds have become of importance in the theory of functorial semi-norms on homology.…

Concise introduction to a relatively new subject of non-linear algebra: literal extension of text-book linear algebra to the case of non-linear equations and maps. This powerful science is based on the notions of discriminant…

For each object in a tensor triangulated category, we construct a natural continuous map from the object's support---a closed subset of the category's triangular spectrum---to the Zariski spectrum of a certain commutative ring of…

In a graph, a matching cut is an edge cut that is a matching. Matching Cut is the problem of deciding whether or not a given graph has a matching cut, which is known to be NP-complete even when restricted to bipartite graphs. It has been…

The classical notion of retraction map used to approximate geodesics is extended and rigorously defined to become a powerful tool to construct geometric integrators and it is called discretization map. Using the geometry of the tangent and…

We give a topological model for a polynomial map from $\C^n$ to $\C$ in the neighborhood of a fiber with isolated singularities. This is motivated out of the ``unfolding of links'' described earlier by the first author and Lee Rudolph. The…

The eigenvalues of companion matrices associated with generalized Lucas sequences, denoted as L, exhibit a striking geometric resemblance to the Mandelbrot set M. This work investigates this connection by analyzing the statistical…

The d-Cut problem is to decide if a graph has an edge cut such that each vertex has at most d neighbours at the opposite side of the cut. If $d=1$, we obtain the intensively studied Matching Cut problem. The d-Cut problem has been studied…