Related papers: Dynamical systems with a parallel tensor

In this article we associate a combinatorial differential graded algebra to a cubic planar graph G. This algebra is defined combinatorially by counting binary sequences, which we introduce, and several explicit computations are provided. In…

This work makes a parallel construction for curves on threefolds to a ``current-theoretic'' proof of Abel's theorem giving the rational equivalence of divisors P and Q on a Riemann surface when Q - P is (equivalent to) zero in the Jacobian…

The dynamical structure of the rational map $ax+1/x$ on the projective line over the field Q2 of $2$-adic numbers, is fully described.

We classify thick tensor ideals of finite objects in the category of rational torus-equivariant spectra, showing that they are completely determined by geometric isotropy. This is essentially equivalent to showing that the Balmer spectrum…

We study linear maps preserving the higher numerical ranges of tensor product of matrices.

We illustrate the rich landscape of 4-manifold topology through the lens of counterexamples. We consider several of the most commonly studied equivalence relations on 4-manifolds and how they are related to one another. We explain…

In this paper, we study CTP maps, that is, marked rational maps with constant Thurston pullback mapping. We prove that all the regular or mixing CTP polynomials satisfy McMullen's condition. Additionally, we construct a new class of…

In this paper, some particular rational maps P_n ---> P_n+1, called quadratic congruences, are studied. They appear in the theory of exceptional vector bundles on projective spaces.

Let G be a connected reductive group defined over a finite field F_q and let L be the Levi subgroup (defined over F_q) of a parabolic subgroup P of G. We define a linear map from class functions on L(F_q) to class functions on G(F_q). This…

We develop some foundations of commutative algebra, with a view towards algebraic geometry, in symmetric tensor categories. Most results establish analogues of classical theorems, in tensor categories which admit a tensor functor to some…

Given a differential or $q$-difference equation $P$ of order $n$, we prove that the set of exponents of a generalized power series solution has its rational rank bounded by the rational rank of the support of $P$ plus $n$. We also prove…

The dynamical degree of a dominant rational map $f:\mathbb{P}^N\rightarrow\mathbb{P}^N$ is the quantity $\delta(f):=\lim(\text{deg} f^n)^{1/n}$. We study the variation of dynamical degrees in 1-parameter families of maps $f_T$. We make a…

We prove additive and multiplicative partition theorems, obtaining combinatorial results for p-quasicyclic groups, where p is a prime number. We also get density results for p-quasicyclic groups via left F{\o}lner sequences of non-empty…

Any counterexample to the two-dimensional Jacobian Conjecture gives a rational map from one projective plane to another. We use some ideas of the Minimal Model Program to study the combinatorial structure of a rational surface, that is…

Let X be a smooth complex projective surface. We prove that for any sufficiently big m there exists a rational dominant map f from X into a complex rational ruled surface Y, such that f is generically finite of degree m and has monodromy…

In this paper we consider families of holomorphic maps defined on subsets of the complex plane, and show that the technique developed in \cite{LSvS1} to treat unfolding of critical relations can also be used to deal with cases where the…

Computing a morph between two drawings of a graph is a classical problem in computational geometry and graph drawing. While this problem has been widely studied in the context of planar graphs, very little is known about the existence of…

Markov partitions persisting in a neighbourhood of hyperbolic components of rational maps were constructed under the condition that closures of Fatou components are disjoint in \cite{R1}. Given such a partition, we characterize all nearby…

We consider reversible vector fields in $\mathbb{R}^{2n}$ such that the set of fixed points of the involutory reversing symmetry is $n$-dimensional. Let such system have a smooth one-parameter family of symmetric periodic orbits which is of…

Let $X$ be a compact metric space and let $f:X\rightarrow X$ be a homeomorphism on $X$. We show that if $f$ is both pointwise recurrent and expansive, then the dynamical system $(X, f)$ is topologically conjugate to a subshift of some…