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Computability and Dynamical Systems

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Part of the Springer Proceedings in Mathematics book series (PROM, volume 1)

Abstract

In this paper we explore results that establish a link between dynamical systems and computability theory (not numerical analysis). In the last few decades, computers have increasingly been used as simulation tools for gaining insight into dynamical behavior. However, due to the presence of errors inherent in such numerical simulations, with few exceptions, computers have not been used for the nobler task of proving mathematical results. Nevertheless, there have been some recent developments in the latter direction. Here we introduce some of the ideas and techniques used so far, and suggest some lines of research for further work on this fascinating topic.

Keywords

Turing Machine Hyperbolic System Strange Attractor Computable Function Reachability Problem 
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Notes

cknowledgements

J. Buescu was partially supported by Fundação para a Ciência e a Tecnologia, Financiamento Base 2009 – ISFL/1/209. D. Graça was partially supported by Fundação para a Ciência e a Tecnologia and EU FEDER POCTI/POCI via SQIG – Instituto de Telecomunicações. DG was also attributed a Taft Research Collaboration grant which made possible a research visit to23pc]Please update references “[11, 16, 22, 23, 24]”. U. Cincinnati. N. Zhong was partially supported by the 2009 Taft Summer Research Fellowship.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.DM/FCULUniversity of LisbonLisbonPortugal
  2. 2.CMAFLisbonPortugal
  3. 3.DM/Faculdade de Ciências e TecnologiaUniversidade do AlgarveFaroPortugal
  4. 4.SQIG/Instituto de TelecomunicaçõesLisbonPortugal
  5. 5.DMS, University of CincinnatiCincinnatiUSA

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