Related papers: Algebraic Entropy of Birational Maps with Invarian…

For any discrete time dynamical system with a rational evolution, we define an entropy, which is a global index of complexity for the evolution map. We analyze its basic properties and its relations to the singularities and the…

We introduce the algebraic entropy for continuous endomorphisms of locally linearly compact vector spaces over a discrete field, as the natural extension of the algebraic entropy for endomorphisms of discrete vector spaces. We show that the…

This work deals with a special case of family of birational maps f : C2 -> C2 dynamically classified in [9]. In this work we study the zero entropy sub families of f. The sequence of degrees dn associated to the iterates of f is found to…

In this article we extract and study the zero entropy subfamilies of a certain family of birational maps of the plane. We find these zero entropy mappings and give the invariant fibrations associated to them.

A method to calculate the algebraic entropy of a mapping which can be lifted to an isomorphism of a suitable rational surfaces (the space of initial values) are presented. It is shown that the degree of the $n$th iterate of such a mapping…

Two important notions of integrability for discrete mappings are algebraic integrability and singularity confinement, have been used for discrete mappings. Algebraic integrability is related to the existence of sufficiently many conserved…

Various limit-free formulas are given for the computation of the algebraic and the topological entropy, respectively in the settings of endomorphisms of locally finite discrete groups and of continuous endomorphisms of totally disconnected…

We extend the definition of algebraic entropy to semi-discrete (difference-differential) equations. Calculating the entropy for a number of integrable and non integrable systems, we show that its vanishing is a characteristic feature of…

We study the directional entropy of the dynamical system associated to a $\Z^2$ configuration in a finite alphabet. We show that under local assumptions on the complexity, either every direction has zero topological entropy or some…

We extend the definition of algebraic entropy to a class of differential-delay equations. The vanishing of the entropy, as a structural property of an equation, signals its integrability. We suggest a simple way to produce…

Usually, it is supposed that irreversibility of time appears only in macrophysics. Here, we attempt to introduce the microphysical arrow of time assuming that at a fundamental level nature could be non-associative. Obtaining numerical…

We illustrate the use of the notion of derived recurrences introduced earlier to evaluate the algebraic entropy of self-maps of projective spaces. We in particular give an example, where a complete proof is still awaited, but where…

We investigate linear parabolic maps on the torus. In a generic case these maps are non-invertible and discontinuous. Although the metric entropy of these systems is equal to zero, their dynamics is non-trivial due to folding of the image…

We give the basic definition of algebraic entropy for lattice equations. The entropy is a canonical measure of the complexity of the dynamics they define. Its vanishing is a signal of integrability, and can be used as a powerful…

A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…

Coarse geometry studies metric spaces on the large scale. The recently introduced notion of coarse entropy is a tool to study dynamics from the coarse point of view. We prove that all isometries of a given metric space have the same coarse…

We study the iterative behavior of the family of 3-step linear fractional recurrences and the family of birational maps they define. We determine all the possible periodicities within this family or, equivalently, the birational maps of…

We study the algebraic entropy of continuous endomorphisms of compactly covered, locally compact, topologically quasihamiltonian groups. We provide a Limit-free formula which helps us to simplify the computations of this entropy. Moreover,…

We prove that any planar birational integrable map, which preserves a fibration given by genus $0$ curves has a Lie symmetry and some associated invariant measures. The obtained results allow to study in a systematic way the global dynamics…

Under the assumption of the gluing orbit property, equivalent conditions to having zero topological entropy are investigated. In particular, we show that a dynamical system has the gluing orbit property and zero topological entropy if and…