相关论文: A transcendental dynamical degree
A set of algorithms is presented for efficient numerical calculation of the time evolution of classical dynamical systems. Starting with a first approximation for solving the differential equations that has a "reversible" character, we show…
Let X be a non-singular projective hypersurface of degree 4, which is defined over the rational numbers. Assume that X has dimension 39 or more, and that X contains a real point and p-adic points for every prime p. Then X is shown to…
A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical…
The $k$-secant degree is studied with a combinatorial approach. A planar toric degeneration of any projective toric surface $X$ corresponds to a regular unimodular triangulation $D$ of the polytope defining $X$. If the secant ideal of the…
Given a countable structure $\mathcal{A}$, the degree spectrum of $\mathcal{A}$ is the set of all Turing degrees which can compute an isomorphic copy of $\mathcal{A}$. One of the major programs in computable structure theory is to determine…
Topological bases of behaviour of trajectories for autonomous differential systems of the second order on the projective phase plane are stated. By means of Poincare's circles the projective atlas of trajectories is constructed.…
Self-inducing structure of pentagonal piecewise isometry is applied to show detailed description of periodic and aperiodic orbits, and further dynamical properties. A Pisot number appears as a scaling constant and plays a crucial role in…
Using a numerical library for arbitrary precision arithmetic I study the irregular dependence of the diffusion coefficient on the slope of a piecewise linear map defining a dynamical system. I find that the graph of the diffusion…
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…
Let R be a two-dimensional regular local ring having an algebraically closed residue field and let a be a complete ideal of finite colength in R. In this article we investigate the jumping numbers of a by means of the dual graph of the…
We address the problem of the maximal finite number of real points of a real algebraic curve (of a given degree and, sometimes, genus) in the projective plane. We improve the known upper and lower bounds and construct close to optimal…
We provide examples of groups with transcendental spectral radius: We first construct finitely presented examples, using links between decidability of the Word Problem and semi-computability of the spectral radius. This argument extends to…
In this paper we present a way of computing the degree of the secant (resp., tangent) variety of a smooth projective surface, under the assumption that the divisor giving the embedding in the projective space is $3$-very ample. This method…
It was shown by A. Beauville that if the canonical map $\varphi_{|K_M|}$ of a complex smooth projective surface $M$ is generically finite, then ${\rm deg}(\varphi_{|K_M|})\leq 36$. The first example of a surface with canonical degree 36 was…
Transcendental numbers play an important role in many areas of science. This paper contains a short survey on transcendental numbers and some relations among them. New inequalities for transcendental numbers are stated in Section 2 and…
We give a survey on classical and recent applications of dynamical systems to number theoretic problems. In particular, we focus on normal numbers, also including computational aspects. The main result is a sufficient condition for…
In this paper we address the following question arising from the work of P. Etingof, D. Kazhdan and A. Polishchuk (math.AG/0003009): given a homogeneous complex polynomial, when the rational map defined by its partials is of degree 1? We…
Let $\phi:X\dashrightarrow X$ be a dominant rational map of a smooth variety and let $x\in X$, all defined over $\bar{\mathbb Q}$. The dynamical degree $\delta(\phi)$ measures the geometric complexity of the iterates of $\phi$, and the…
Given a rational function of degree at least two defined over a number field k, we study the cardinality of the set of rational iterated preimages. We prove bounds for the cardinality of this set as the rational function varies in certain…
The existence of normal deterministic diffusion in dynamical systems with a two-dimensional phase space tiled by regular triangles (or their unions into regular hexagons) is proven.