Related papers: Dynatomic cycles for morphisms of projective varie…
Here we investigate the birational geometry of projective varieties of arbitrary dimension having defective higher secant varieties. We apply the classical tool of tangential projections and we determine natural conditions for uniruledness,…
The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…
We prove the functoriality for proper push-forward of the characteristic cycles of constructible complexes by morphisms of smooth projective schemes over a perfect field, under the assumption that the direct image of the singular support…
Random walks of particles on a lattice are a classical paradigm for the microscopic mechanism underlying diffusive processes. In deterministic walks, the role of space and time can be reversed, and the microscopic dynamics can produce quite…
Models of period variations are basic tools for period analyzes of variable stars. We introduce phase function and instant period and formulate basic relations and equations among them. Some simple period models are also presented.
Functions whose symmetries form a crystallographic group in particular have a lattice of periods, and the set of their level curves forms a periodic pattern. We show how after projecting these functions, one obtains new functions with a…
We study directed random graphs (random graphs whose edges are directed) as they evolve in discrete time by the addition of nodes and edges. For two distinct evolution strategies, one that forces the graph to a condition of near acyclicity…
We introduce the notion of a categorical cone, which provides a categorification of the classical cone over a projective variety, and use our work on categorical joins to describe its behavior under homological projective duality. In…
The existence, uniqueness, and asymptotic stability of modulo periodic Poisson stable solutions of dynamic equations on a periodic time scale are investigated. The model under investigation involves a term which is constructed via a Poisson…
By computing all cyclotomic points on some algebraic varieties, we get an independent and efficient way to find all rational $a^3b$-monotiles for the sphere, thereby completing the classification of edge-to-edge monohedral quadrilateral…
The topology of periodic spaces has attracted a lot of interest in recent years in order to study and classify crystalline structures and other large homogeneous data sets, such as the distribution of galaxies in cosmology. In practice,…
A step forward is made in a long standing Lov\'{a}sz's problem regarding hamiltonicity of vertex-transitive graphs by showing that every connected vertex-transitive graph of order a product of two primes, other than the Petersen graph,…
We show the existence of canonical heights of subvarieties for bounded sequences of morphisms and give some applications.
The dynamical degree $\lambda(f)$ of a birational transformation $f$ measures the exponential growth rate of the degree of the formulae that define the $n$-th iterate of $f$. We study the set of all dynamical degrees of all birational…
We study finite morphisms of varieties and the link between their top multiplicity loci under certain assumptions. More precisely, we focus on how to determine that link in terms of the spaces of arcs of the varieties.
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…
Linear finite dynamical systems play an important role, for example, in coding theory and simulations. Methods for analyzing such systems are often restricted to cases in which the system is defined over a field %and usually strive to…
We characterize universally generalizing morphisms which satisfy descent of algebraic cycles integrally as those universally generalizing morphisms which are surjective with generically reduced fibres. In doing so, we introduce a naive…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
In our previous paper an effective algorithm for inverting polynomial automorphisms was proposed. We extend its application to the case of formal power series over a field of arbitrary characteristic and illustrate the proposed approach…