相关论文: B\"ottcher coordinates at superattracting fixed po…

In this work we investigate the topological information captured by the Euler obstruction of a map, $f:(X,0)\to (\mathbb{C}^{2},0)$, with $(X,0)$ a germ of a complex $d$-equidimensional singular space, with $d > 2$, and its relation with…

We study jets of germs of holomorphic maps between two strongly pseudoconvex domains under the condition that the image of one domain is contained into the other and a given boundary point is (non-tangentially) mapped to a given boundary…

We characterize those complete commutative positive linear ordered monoids $W$ such that whenever $f$ is a map from a Cauchy complete $W$-metric space to itself, the existence of a fixed point of $f$ is independent of the background model…

Let $\Delta ^{2}$ be a ball in the complex vector space $\mathbb{C}^{2}$ centered at the origin, let $f:\Delta ^{2}\to \mathbb{C}^{2}$ be a holomorphic mapping$,$ with $f(0)=0$, and let $M$ be a positive integer. If the origin 0 is an…

We show that a closed subscheme of a given locally noetherian scheme can be constructed by prescribing it germs at all points of the ambient scheme in a manner consistent with specialization of points, provided the resulting set of all…

We consider semidifferentiable (possibly nonsmooth) maps, acting on a subset of a Banach space, that are nonexpansive either in the norm of the space or in the Hilbert's or Thompson's metric inherited from a convex cone. We show that the…

Let $R$ be a ring of characteristic $0$ with field of fractions $K$, and let $m\ge2$. The B\"ottcher coordinate of a power series $\varphi(x)\in x^m + x^{m+1}R[\![x]\!]$ is the unique power series $f_\varphi(x)\in x+x^2K[\![x]\!]$…

Affine superspace $\mathbb{C}^{1 \mid n}$ has a single bosonic coordinate $z$ and $n$ fermionic coordinates $\theta_1, \dots, \theta_n$. Let $M$ be the supertorus obtained by quotienting $\mathbb{C}^{1 \mid n}$ by the abelian group…

The Schwarz lemmas are well-known characterizations for holomorphic maps and we exhibit two examples of their applications. For a sequence family of biholomorphisms $f_j$, it is useful to determine the location of $f_j(q)$ for a fixed point…

When we consider a proper holomorphic map \ $\tilde{f}: X \to C$ \ of a complex manifold \ $X$ \ on a smooth complex curve \ $C$ \ with a critical value at a point \ $0$ \ in \ $C$, the choice of a local coordinate near this point allows to…

Let $B$ be a M\"obius band and $f:B \to \mathbb{R}$ be a Morse map taking a constant value on $\partial B$, and $\mathcal{S}(f,\partial B)$ be the group of diffeomorphisms $h$ of $B$ fixed on $\partial B$ and preserving $f$ in the sense…

Skew morphisms, which generalise automorphisms for groups, provide a fundamental tool for the study of regular Cayley maps and, more generally, for finite groups with a complementary factorisation $G=BY$, where $Y$ is cyclic and core-free…

After recalling the definition of codes as modules over skew polynomial rings, whose multiplication is defined by using an automorphism and a derivation, and some basic facts about them, in the first part of this paper we study some of…

Given a smooth, open, oriented surface $X$ endowed with a family of complex structures $\{J_b\}_{b\in B}$ depending continuously on the parameter $b$ in a metrisable space $B$, we construct a continuous family of proper holomorphic maps…

We use Cramer's formula for the inverse of a matrix and a combinatorial expression for the determinant in terms of paths of an associated digraph (which can be traced back to Coates) to give a combinatorial interpretation of M\"obius…

The critical loci of a map $f:X\to Y$ between smooth schemes over a field $k$ are the locally closed subschemes $\Sigma^i(f)\subseteq X$ where the differential of $f$ has constant rank. We prove that if $f : X\to \mathbb A^r$ is the general…

A topological space has the fixed point property if every continuous self-map of that space has at least one fixed point. We demonstrate that there are serious restraints imposed by the requirement that there be a choice of fixed points…

We prove that a closed convex subset $C$ of a real Hilbert space $X$ has the fixed point property for $(c)$-mappings if and only if $C$ is bounded. Some convergence results about the iterations are obtained.

For $\tau>2$, let $T$ be a $C^\tau$ skew product map of the form $(x+\alpha,y+h(x))$ on $\mathbb T^2$ over a rotation of the circle. We show that if $T$ preserves a measurable section, then it is disjoint to the M\"{o}bius sequence. This in…

In this paper, we give some requirements under which two self-mappings have a common fixed point in $b$-metric-like spaces.