Related papers: Iterated Images and the Plane Jacobian Conjecture

We consider certain matrix-products where successive matrices in the product belong alternately to a particular qualitative class or its transpose. The main theorems relate structural and spectral properties of these matrix-products to the…

For a field K, rational function phi in K(z) of degree at least two, and alpha in P^1(K), we study the polynomials in K[z] whose roots are given by the solutions to phi^n(z) = alpha, where phi^n denotes the nth iterate of phi. When the…

In this paper we study the orthogonality conditions satisfied by Jacobi polynomials $P_n^{(\alpha,\beta)}$ when the parameters $\alpha$ and $\beta$ are not necessarily $>-1$. We establish orthogonality on a generic closed contour on a…

We introduce and study a deformation of commutative polynomial algebras in even numbers of variables. We also discuss some connections and applications of this deformation to the generalized Laguerre orthogonal polynomials and the…

We study the interaction between two structures on the group of polynomial automorphisms of the affine plane: its structure as an amalgamated free product and as an infinite-dimensional algebraic variety. We introduce a new conjecture, and…

In this paper we introduce the notion of infinite dimensional Jacobi structure to describe the geometrical structure of a class of nonlocal Hamiltonian systems which appear naturally when applying reciprocal transformations to Hamiltonian…

We study the bispectrality of Jacobi type polynomials, which are eigenfunctions of higher-order differential operators and can be defined by taking suitable linear combinations of a fixed number of consecutive Jacobi polynomials. Jacobi…

This paper studies geometric properties of the Iterated Matrix Multiplication polynomial and the hypersurface that it defines. We focus on geometric aspects that may be relevant for complexity theory such as the symmetry group of the…

In the paper, we first classify all polynomial maps of the form $H=(u(x,y,z),v(x,y,z), h(x,y))$ in the case that $JH$ is nilpotent and $\deg_zv\leq 1$. After that, we generalize the structure of $H$ to…

We prove the equivalence of the Jacobian Conjecture (JC(n)) and the Conjecture on the cardinality of the set of fixed points of a polynomial nilpotent mapping (JN(n)) and prove a series of assertions confirming JN(n).

We first give a characterization for Mathieu subspaces of univariate polynomial algebras over fields in terms of their radicals. We then deduce that for some classes of classical univariate orthogonal polynomials the Image Conjecture is…

Let $F:\Bbb C^n\to\Bbb C^n$ be a polynomial mapping with a non vanishing Jacobian. If the set $S_F$ of non-properness of $F$ is smooth, then $F$ is a surjective mapping. Moreover, the set $S_F$ can not be connected (this is the…

Let $SU_X(n,L)$ be the moduli space of rank n semistable vector bundles with fixed determinant L on a smooth projective genus g curve X. Let $SU_X^s(n,L)$ denote the open subset parametrizing stable bundles. We show that if g>3 and n > 1,…

We study the sets of planes in an even dimensional real vector space $V$ which are simultaneously stabilised by a pair of complex structures on $V$. We completely describe these sets of planes for pairs of orthogonal complex structures.…

We consider a family of steady free-surface flow problems in two dimensions, concentrating on the effect of nonlinearity on the train of gravity waves that appear downstream of a disturbance. By exploiting standard complex variable…

In recent work on holomorphic maps that are symmetric under certain complex reflection groups---generated by complex reflections through a set of hyperplanes, the author announced a general conjecture related to reflection groups. The claim…

In this paper we prove that if $f$ is a self-mapping of a nonempty subset $K$ of a normed space $X$ that satisfies some mild conditions, then the minimal displacement of large iterations $f^n$ always dominates that of $f$ along certain…

This paper examines and strengthens the Cuntz-Thomsen picture of equivariant Kasparov theory for arbitrary second-countable locally compact groups, in which elements are given by certain pairs of cocycle representations between C*-dynamical…

Algebraic K-theory is the stable homotopy theory of homotopy theories, and it interacts with algebraic structures accordingly. In particular, we prove the Deligne Conjecture for algebraic K-theory.

We relate the equianalytic and the equisingular deformations of a reduced complex plane curve to the Jacobian syzygies of its defining equation. Several examples and conjectures involving rational cuspidal curves are discussed.