Related papers: Block Maps between Primitive Uniform and Pisot Sub…

Biological systems exhibit a continuous stream of movements, consisting of sequential segments, that allow them to perform complex tasks in a creative and versatile fashion. This observation has led researchers towards identifying…

In this article we prove first of all the nonexistence of holomorphic submersions other than covering maps between compact quotients of complex unit balls, with a proof that works equally well in a more general equivariant setting. For a…

Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of…

We show how positive unital linear maps can be used to obtain lower bounds for the maximum distance between the eigenvalues of two normal matrices. Some related bounds for the spread and condition number of Hermitian matrices are also…

For a map of the unit interval with an indifferent fixed point, we prove an upper bound for the variance of all observables of $n$ variables $K:[0,1]^n\to\R$ which are componentwise Lipschitz. The proof is based on coupling and decay of…

We define a map between the set of permutations that avoid either the four patterns $3214,3241,4213,4231$ or $3124,3142,4123,4132$, and the set of Dyck prefixes. This map, when restricted to either of the two classes, turns out to be a…

We study stationary ordered Bratteli diagrams and give necessary and sufficient conditions for these orders to generate a continuous Vershik map. We apply this to finding adic representations for one sided substitution subshifts. We give an…

We obtain an analog of the prime number theorem for a class of branched covering maps on the $2$-sphere $S^2$ called expanding Thurston maps, which are topological models of some non-uniformly expanding rational maps without any smoothness…

Tilings and point sets arising from substitutions are classical mathematical models of quasicrystals. Their hierarchical structure allows one to obtain concrete answers regarding spectral questions tied to the underlying measures and…

The dominant rational maps of finite degree from a fixed variety to varieties of general type, up to birational isomorphisms, form a finite set. This has been known as the Iitaka-Severi conjecture, and is nowdays an established result, in…

We prove the existence of an effective universal upper bound for the order of any integral periodic orbit of any integral algebraic dynamical system in a fixed ambient space. Using this, we demonstrate the decidability of periodicity in…

We prove that a primitive harmonic map is equivariant if and only if it admits a holomorphic potential of degree one. We investigate when the equivariant harmonic map is periodic, and as an application discuss constant mean curvature…

Since the end of the XIXth century, we know that each birational map of the complex projective plane is the product of a finite number of quadratic birational maps of the projective plane; this motivates our work which essentially deals…

We study the central objects of symbolic dynamics, that is, subshifts and block maps, from the perspective of basic category theory, and present several natural categories with subshifts as objects and block maps as morphisms. Our main…

We discuss the bifurcation structure of homoclinic orbits in bimodal one dimensional maps. The universal structure of these bifurcations with singular bifurcation points and the web of bifurcation lines through the parameter space are…

We classify the finite primitive groups containing a permutation with at most four cycles (including fixed points) in its disjoint cycle representation.

We evaluate the variance of coefficients of the characteristic polynomial for binary quantum graphs using a dynamical approach. This is the first example where a spectral statistic can be evaluated in terms of periodic orbits for a system…

Let $C(\mathbf I)$ be the set of all continuous self-maps from ${\mathbf I}=[0,1]$ with the topology of uniformly convergence. A map $f\in C({\mathbf I})$ is called a transitive map if for every pair of non-empty open sets $U,V$ in…

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…

The uniform one-dimensional fragment of first-order logic was introduced a few years ago as a generalization of the two-variable fragment of first-order logic to contexts involving relations of arity greater than two. Quantifiers in this…