Related papers: Structure des homeomorphismes de Brouwer

For a given branched covering between closed connected surfaces, there are several easy relations one can establish between the Euler characteristics of the surfaces, their orientability, the total degree, and the local degrees at the…

This paper introduces two new abstract morphs for two $2$-dimensional shapes. The intermediate shapes gradually reduce the Hausdorff distance to the goal shape and increase the Hausdorff distance to the initial shape. The morphs are…

We show that manifolds which parameterize values of first integrals of integrable finite-dimensional bihamiltonian systems carry a geometric structure which we call a {\em Kronecker web}. We describe two functors between Kronecker webs and…

This article deals with the study of the birational transformations of the projective complex plane which leave invariant an irreducible algebraic curve. We try to describe the state of art and provide some new results on this subject.

We present a sufficient condition for three-dimensional diffeomorphisms having heterodimensional cycles to be approximated arbitrarily well by diffeomorphisms with non-trivial contracting wandering domains via several perturbations. The key…

We provide first a categorical exploration of, and then completion of the mapping of the relationships among, three fundamental perspectives on binary relations: as the incidence matrices of hypergraphs, as the formal contexts of concept…

We study a class of chainable continua which contains, among others, all inverse limit spaces generated by a single interval bonding map which is piecewise monotone and locally eventually onto. Such spaces are realized as attractors of…

Given a pre-monotone Lagrangian link, we obtain Hofer energy estimates for Hamiltonian diffeomorphisms preserving it. Such estimates depend on the braid type of the Hamiltonian diffeomorphism only, and the natural language to talk about…

This paper extends the univariate Theory of Connections, introduced in (Mortari,2017), to the multivariate case on rectangular domains with detailed attention to the bivariate case. In particular, it generalizes the bivariate Coons surface,…

This paper helps to clarify the status of cylindrical contact homology, a conjectured contact invariant introduced by Eliashberg, Givental, and Hofer in 2000. We explain how heuristic arguments fail to yield a well-defined homological…

The well-known Reifenberg theorem states that if a subset of $\mathbb{R}^n$ can be well approximated by $k$-planes at every point and every scale, then it is biH\"older homeomorphic to a $k$-disk. This article concerns a subset $S$ of…

Given a set of points in the plane, we want to establish a connection network between these points that consists of several disjoint layers. Motivated by sensor networks, we want that each layer is spanning and plane, and that no edge is…

Linear fractional transformations on the extended complex plane are classified up to topological conjugacy. Recall that two transformations f and g are called topologically conjugate if there exists a homeomorphism h such that hg=fh.

Let $\Diffeo=\Diffeo(\R)$ denote the group of infinitely-differentiable diffeomorphisms of the real line $\R$, under the operation of composition, and let $\Diffeo^+$ be the subgroup of diffeomorphisms of degree +1, i.e.…

Subsets of a matrix algebra over a field that are invariant under conjugation and contain the linear span of each two of their commuting elements are described. They obviously include the subsets of diagonalizable and nilpotent matrices. In…

We study the mixed formulation of the abstract Hodge Laplacian on axisymmetric domains with general data through Fourer-finite-element-methods in weighted functions spaces. Closed Hilbert complexes and commuting projectors are used through…

We describe a self-homeomorphism $R$ of the Cantor set $X$ and then show that its conjugacy class in the Polish group $H(X)$ of all homeomorphisms of $X$ forms a dense $G_\delta$ subset of $H(X)$. We also provide an example of a locally…

A wandering domain for a diffeomorphism is an open connected set whose iterates are pairwise disjoint. We endow A^n = T^n x R^n with its usual exact symplectic structure. An integrable diffeomorphism {\Phi}^h, i.e. the time-one map of a…

The Reeb space of a smooth map whose codimension is minus is the space defined as the space of all connected components of inverse images. For generic maps such as Morse functions and their higher dimensional versions, they are polyhedra…

We generalize the notion of harmonic conjugate functions and Hilbert transforms to higher dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These conjugate functions are in general far from being…