Invariants on compact spaces

From the dynamical point of view, topological invariants are those characteristics on compact topological spaces which are kept by topological conjugacy. In this paper we consider three of them of special interest: topological entropy, sequence topological entropy and rotational entropy. We survey some of their properties and obtain some useful formulas to their computation over the space of continuous maps on the compact space

Algunos resultados sobre periodicidad global de ecuaciones en diferencias de orden dos y tres

En esta nota repasamos algunos resultados sobre periodicidad global en ecuaciones (autónomas) en diferencias finitas de órdenes dos y tres, y aportamos algún modesto avance en el tema

Origen, motivación y resultados sobre dos ecuaciones en diferencias no lineales

Las ecuaciones en diferencias no lineales xn+1xn−1 − 1 = xn, n ≥ 1 xn+2 = x 2 n (xn+1 − 2) + 2, n ≥ 1 tienen su origen y motivación en problemas de distinta naturaleza. La primera, en un problema de números propuesto por Lyness en 1942 y otro de geometrí de frieze patterns estudiado y resuelto por Coxeter en 1971. La segunda aparece mediante un modelo para describir las propiedades de conducción y de aislamiento eléctrico de quasi-cristales, mediante una red de tipo ”Thue-Morse”. En ambos casos precisaremos algunos aspectos relevantes de su deducción y daremos algunos resultados sobre su comportamiento

Recent developments in dynamical systems: three perspectives

This paper aims to an present account of some problems considered in the past years in Dynamical Systems, new research directions and also provide some open problems

Studies on dendrites and the periodic-recurrent property

In this paper we evidence the interest of considering three outstanding examples of dendrites with different structures, dendrites F!, W and G3. When a dendrite X contains a topological copy of one of them, then it is derived important properties. For example, if X does not contain a topological copy neither F! nor W, then X is a tree. If X does not contain a topological copy of G3 then we obtain that X verifies the Periodic-Recurrent Property (the PR Property) which for dendrites is relevant under the point of view of Topological Dynamics. As an application of the former results, we give a unified proof of the fact that compact intervals of the real line [a; b] (a .= b), arcs and trees have also the PR Property

Sumabilidad en espacios topológicos : Funciones continuas casi convergentes / Francisco Balibrea Gallego; director, Gabriel Vera Botí.

Tesis-Universidad de Murcia.Consulte la tesis en: BCA. GENERAL. ARCHIVO UNIVERSITARIO. TM 3807

Commutativity and non-commutativity of the topological sequence entropy

In this paper we study the commutativity property for topological sequence entropy. We prove that if $X$ is a compact metric space and $f,g: X\rightarrow X$ are continuous maps then $h _A(f\circ g)=h_A(g\circ f)$ for every increasing sequence $A$ if $X=[0,1]$, and construct a counterexample for the general case. In the interim, we also show that the equality $h_A(f)=h_A(f\vert _{\cap _{n\ge 0}f^n(X)})$ is true if $X=[0,1]$ but does not necessarily hold if $X$ is an arbitrary compact metric space.This paper has been partially supported by the D.G.C.Y.T. grant PB95-1004 and the grants COM-20/96 MAT and PB/2/fs/97 (Fundación Séneca, Comunidad Autónoma de Murcia