Aplicaciones de la cohomología de Alexander-Spanier en dinámica discreta

  1. NIEVES RIVERA, DAVID JESUS
Supervised by:
  1. Luis Hernández-Corbato Director
  2. Jaime J. Sánchez Gabites Director
  3. Francisco Romero Ruiz del Portal Director

Defence university: Universidad Complutense de Madrid

Fecha de defensa: 23 March 2023

Committee:
  1. José Manuel Rodríguez Sanjurjo Chair
  2. Manuel Alonso Morón Secretary
  3. Héctor Barge Yáñez Committee member
  4. Alvaro Martínez Perez Committee member
  5. Luis Javier Hernández Paricio Committee member

Type: Thesis

Abstract

In this work, we relate the eigen values and the eigen vectors of the induced map by a continuous map f : X → X on homology or cohomology to dynamic properties of the dynamical system (X, f).The theories that best fit to this problem are ˇCech's because they are the most suitable for describing spaces with bad local properties that are commun situations in dynamic, for example, strange attractors. To address the previous problem, we use intrisic approximations of ˇCech homology and cohomology (we do not go through the simplicial complex to build the chain or cochain complex) like those given in [Giraldo, Mor´on, Ruiz del Portal, y Sanjurjo(2001)] and [Spanier(1948)], respectively, that we develop in the Chapter 1. Also we describe in detail the 0th and the 1st ˇCechhomology groups, and the 0th ˇCech cohomology group...