Set arithmetic and the enclosing problem in dynamics

Marian Mrozek; Piotr Zgliczyński

Annales Polonici Mathematici (2000)

  • Volume: 74, Issue: 1, page 237-259
  • ISSN: 0066-2216

Abstract

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We study the enclosing problem for discrete and continuous dynamical systems in the context of computer assisted proofs. We review and compare the existing methods and emphasize the importance of developing a suitable set arithmetic for efficient algorithms solving the enclosing problem.

How to cite

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Mrozek, Marian, and Zgliczyński, Piotr. "Set arithmetic and the enclosing problem in dynamics." Annales Polonici Mathematici 74.1 (2000): 237-259. <http://eudml.org/doc/208369>.

@article{Mrozek2000,
abstract = {We study the enclosing problem for discrete and continuous dynamical systems in the context of computer assisted proofs. We review and compare the existing methods and emphasize the importance of developing a suitable set arithmetic for efficient algorithms solving the enclosing problem.},
author = {Mrozek, Marian, Zgliczyński, Piotr},
journal = {Annales Polonici Mathematici},
keywords = {dynamical systems; interval arithmetic; rigorous numerical analysis; enclosing problem; computer assisted proofs; set arithmetic},
language = {eng},
number = {1},
pages = {237-259},
title = {Set arithmetic and the enclosing problem in dynamics},
url = {http://eudml.org/doc/208369},
volume = {74},
year = {2000},
}

TY - JOUR
AU - Mrozek, Marian
AU - Zgliczyński, Piotr
TI - Set arithmetic and the enclosing problem in dynamics
JO - Annales Polonici Mathematici
PY - 2000
VL - 74
IS - 1
SP - 237
EP - 259
AB - We study the enclosing problem for discrete and continuous dynamical systems in the context of computer assisted proofs. We review and compare the existing methods and emphasize the importance of developing a suitable set arithmetic for efficient algorithms solving the enclosing problem.
LA - eng
KW - dynamical systems; interval arithmetic; rigorous numerical analysis; enclosing problem; computer assisted proofs; set arithmetic
UR - http://eudml.org/doc/208369
ER -

References

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  18. [18] P. Zgliczyński, Remarks on computer assisted proof of chaotic behavior in ODE's, in preparation. 

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