TOPDS

Topological dynamics and chaos on compact metric spaces

 Coordinatore UNIVERSIDAD DE MURCIA 

 Organization address address: AVENIDA TENIENTE FLOMESTA S/N - EDIFICIO CONVALECENCIA
city: MURCIA
postcode: 30003

contact info
Titolo: Dr.
Nome: Francisco
Cognome: Balibrea Gallego
Email: send email
Telefono: 00 34 968 367625
Fax: 00 34 968 367 625

 Nazionalità Coordinatore Spain [ES]
 Totale costo 151˙568 €
 EC contributo 151˙568 €
 Programma FP7-PEOPLE
Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
 Code Call FP7-PEOPLE-2007-2-1-IEF
 Funding Scheme MC-IEF
 Anno di inizio 2009
 Periodo (anno-mese-giorno) 2009-03-01   -   2011-02-28

 Partecipanti

# participant  country  role  EC contrib. [€] 
1    UNIVERSIDAD DE MURCIA

 Organization address address: AVENIDA TENIENTE FLOMESTA S/N - EDIFICIO CONVALECENCIA
city: MURCIA
postcode: 30003

contact info
Titolo: Dr.
Nome: Francisco
Cognome: Balibrea Gallego
Email: send email
Telefono: 00 34 968 367625
Fax: 00 34 968 367 625

ES (MURCIA) coordinator 151˙568.66

Mappa


 Word cloud

Esplora la "nuvola delle parole (Word Cloud) per avere un'idea di massima del progetto.

mixing    smital    extend    paper    maps    lines    dynamics    theory    topds    he    chaos    collaborations    notions    successes    equations    topological    meetings    phenomena    researcher    dynamical    chaotic    scrambled    spaces    distributional    graphs    complexity    relations    international    scientific    independent    distributionally    dimension   

 Obiettivo del progetto (Objective)

'In the paper 'Measure of chaos and a spectral decomposition of dynamical systems of interval' (which extends Li and Yorke approach stated in their famous paper 'Period three implies chaos') Schweizer and Smital introduced the definition of distributional chaos. Scientific aim of this project is to study distributional chaos and its relations to other notions known from Topological Dynamics. Main problems we will cosider are the following: - how 'large' distributionally scrambled sets can be form topological, measure theoretic or dimension theory point of view? - what are sufficient conditions (topological mixing, specification property, topological exactness, shadowing) to ensure distributional scrambled sets being uncountable, perfect, invariant, etc. ? - what are condition not strong enough to imply distributional chaos in general case (e.g. it is known that positive topological entropy or weak mixing belongs to this class)? - are there any other spaces (graphs, dendrites, low-dimensional continua) which guarantee equivalent conditions from Schwaizer and Smital paper to hold (it is known that there is no equivalence in general, in particular in dimension two or zero)? Additionally, we will study shift spaces and their generalizations for a better understanding of the notion of 'complexity' in the theory of dynamical systems. The research undertaken in this project aims to extend knowledge about chaotic phenomena in dynamical systems. The main aim of the project is to extend knowledge and research experience of the researcher to the level that he is able to prepare his habilitation thesis. The researcher will present obtained results at international meetings. He will extend his scientific collaborations and start new independent lines of research in his career.'

Introduzione (Teaser)

An EU-funded research initiative supported researcher-directed study of topological dynamics and distributional chaos. Various project successes contributed to advances in this scientific area.

Descrizione progetto (Article)

The 'Topological dynamics and chaos on compact metric spaces' (TOPDS) project had as its scientific focus the study of distributional chaos and its relations to other notions of topological dynamics. The goal was to extend knowledge about chaotic phenomena in dynamical systems, and at the same time to expand the knowledge and research experience of the researcher.

Over the course of the project, the researcher achieved a number of successful results, which were to be presented at international meetings. He was also tasked with extending scientific collaborations and starting on new independent lines of research.

The technique used to prove that it is possible to transfer a distributionally scrambled set from factor to extension was also used to investigate the dynamics of non-autonomous differential equations. Other TOPDS successes include the development of a formal method of measuring complexity of these equations which, in this context, provided a strict edge between chaotic and non-chaotic dynamics.

Activities also resulted in delivery of a method for constructing continuous maps and obtaining elementary proofs relevant to dense periodicity for maps on topological graphs and on specific spaces.

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