TOPDSC

Topological aspects of dynamical independence and chaos

Coordinatore	INSTYTUT MATEMATYCZNY POLSKIEJ AKADEMII NAUK.    more  Organization address address: ul. Sniadeckich 8 city: WARSZAWA postcode: 956 contact info Titolo: Prof. Nome: Tadeusz Cognome: Januszkiewicz Email: send email Telefono: +48 22 5228110
Nazionalità Coordinatore	Poland [PL]
Totale costo	45˙000 €
EC contributo	45˙000 €
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-2010-RG
Funding Scheme	MC-ERG
Anno di inizio	2011
Periodo (anno-mese-giorno)	2011-05-01   -   2014-04-30

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	INSTYTUT MATEMATYCZNY POLSKIEJ AKADEMII NAUK.  Organization address address: ul. Sniadeckich 8 city: WARSZAWA postcode: 956 contact info Titolo: Prof. Nome: Tadeusz Cognome: Januszkiewicz Email: send email Telefono: +48 22 5228110	PL (WARSZAWA)	coordinator	45˙000.00

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 Obiettivo del progetto (Objective)

'The aim of this project is the study of complicated, chaotic dynamics. In the project we will investigate local aspects of dynamics, like dynamics of pairs, n-tuples, or dynamics over sets. Particular, we will be interested in pairs chaotic in the sense of Li and Yorke, entropy pairs, independent sets, etc. We will search for connections between shadowing property and chaos, especially these that can be used successfully in applications. In our research we will combine tools like covering relations or tools related with residual sets like in methods of Mycielski and Kuratowski, with analytical methods and rigorous treatment of systems arising in concrete problems.'

Introduzione (Teaser)

Things that are impossible to predict or control such as the weather, the stock market or brain state fall under the umbrella of chaos. EU-funded scientists extended techniques to detect chaos with a number of novel characterisations.

Descrizione progetto (Article)

Chaos theory describes the behaviours of complex systems, those with so many moving elements that it is impossible to begin to explain the dynamics without powerful computers. Despite their seeming unpredictability, the behaviours of these systems are not completely random and, in the everyday use of the word, chaotic. Rather, they are deterministic and non-linear.

However, because they are complex, we can never know all the initial conditions of the system in sufficient detail to define the evolution of the states of the system. Because they also exhibit sensitive dependence, meaning that a very small change in initial conditions can cause drastic changes in output, lack of knowledge about the initial conditions can lead to, well, chaos.

Within the scope of the project 'Topological aspects of dynamical independence and chaos' (TOPDSC), EU-funded scientists extended the mathematics used to detect whether a system is chaotic. They examined local and global properties and interactions among elements in certain mathematical (compact metric) spaces.

The emphasis was on the global property of chaotic mixing, in particular in relation to fluid flow. Scientists developed characterisations of the local aspects of mixing expressed in terms of weakly mixing sub-spaces. Among the many results were a relation between weakly mixing sets and various types of chaos. The team also studied definitions of chaos in terms of local aspects such as pairs and n-tuples, ordered sequences of elements in which n is a non-negative integer.

TOPDSC discovered many new phenomena and mathematical descriptions in chaos theory and proved the practicality of their results. With a focus on successful application of results, the project has extended understanding of topological aspects of chaos in systems with complicated dynamics.