Related papers: Recoding the Classic H\'enon-Devaney Map

We introduce a class of maps from an affine flat into a Riemannian manifold that solve an elliptic system defined by the natural second order elliptic operator of the affine structure and the nonlinear Riemann geometry of the target. These…

We present a structural approach of some results about jumps in the behavior of the profile (alias generating function) of hereditary classes of finite structures. We start with the following notion due to N.Thi\'ery and the second author.…

Structural properties of finite digraphs $R$ and $S$ are studied which enforce $\# {\cal H}(G,R) \leq \# {\cal H}(G,S)$ for every finite digraph $G \in \mathfrak{ D }'$, where ${\cal H}(G,H)$ is the set of homomorphisms from $G$ to $H$, and…

We generalise the concept of duality to systems of ordinary difference equations (or maps). We propose a procedure to construct a chain of systems of equations which are dual, with respect to an integral $H$, to the given system, by…

This paper revisits the notion of classical orthogonal polynomials from a broader functional-analytic point of view. It is intended neither as a survey of known results nor as a review of the literature, but rather as a conceptual…

A Thurston map is a branched covering map $f\colon S^2\to S^2$ that is postcritically finite. Mating of polynomials, introduced by Douady and Hubbard, is a method to geometrically combine the Julia sets of two polynomials (and their…

Dehn twists around simple closed curves in oriented surfaces satisfy the braid relations. This gives rise to a group theoretic from the braid group to the mapping class group. We prove here that this map is trivial in stable homology with…

We study conjugacy invariants for completely positive maps that are inspired by the concept of curvature introduced for commuting d-tuples of contractions by Arveson

We investigate in detail the connection between harmonic maps from Riemann surfaces into the unitary group $\U(n)$ and their Grassmannian models: these are families of shift-invariant subspaces of $L^2(S^1,\C^n)$. With the help of…

We describe dynamical properties of a map $\mathfrak{F}$ defined on the space of rational functions. The fixed points of $\mathfrak{F}$ are classified and the long time behavior of a subclass is described in terms of Eulerian polynomials.

Let H: C^2 -> C^2 be the Henon mapping given by (x,y) --> (p(x) - ay,x). The key invariant subsets are K_+/-, the sets of points with bounded forward images, J_+/- = the boundary of K_+/-, J = the union of J_+ and J_-, and K = the union of…

For quantum systems described by finite matrices, linear and affine maps of matrices are shown to provide equivalent descriptions of evolution of density matrices for a subsystem caused by unitary Hamiltonian evolution in a larger system;…

This paper is about the study of F-transforms based on overlap and grouping maps, residual and co-residual implicator over complete lattice from both constructive and axiomatic approaches. Further, the duality, basic properties, and the…

Suppose we are given a graph and want to show a property for all its cycles (closed chains). Induction on the length of cycles does not work since sub-chains of a cycle are not necessarily closed. This paper derives a principle reminiscent…

We propose an inverse approach for dealing with interval maps based on the manner whereby their branches are related (folding property), instead of addressing the map equations as a whole. As a main result, we provide a symmetry-breaking…

After defining generalizations of the notions of covariant derivatives and geodesics from Riemannian geometry for reductive Cartan geometries in general, various results for reductive Cartan geometries analogous to important elementary…

This paper discusses a more general contractive condition for a class of extended cyclic self-mappings on the union of a finite number of subsets of a metric space which are allowed to have a finite number of successive images in the same…

In this paper, we show that for finite $CW$-complexes $X$ and two-stage space $Y$ (for example $n$-spheres $S^n$, homogeneous spaces and $F_0$-spaces), the rational homotopy type of $\map(X, Y)$ is determined by the cohomology algebra…

We compute the trace of an endomorphism in equivariant bivariant K-theory for a compact group G in several ways: geometrically using geometric correspondences, algebraically using localisation, and as a Hattori-Stallings trace. This results…

We give a combinatorial classification for the class of postcritically fixed Newton maps of polynomials and indicate potential for extensions. As our main tool, we show that for a large class of Newton maps that includes all hyperbolic…