Reconstructing the global dynamics of attractors via the Conley index

Christopher McCord

Banach Center Publications (1999)

  • Volume: 47, Issue: 1, page 145-156
  • ISSN: 0137-6934

Abstract

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Given an unknown attractor 𝓐 in a continuous dynamical system, how can we discover the topology and dynamics of 𝓐? As a practical matter, how can we do so from only a finite amount of information? One way of doing so is to produce a semi-conjugacy from 𝓐 onto a model system 𝓜 whose topology and dynamics are known. The complexity of 𝓜 then provides a lower bound for the complexity of 𝓐. The Conley index can be used to construct a simplicial model and a surjective semi-conjugacy for a large class of attractors. The essential features of this construction are that the model 𝓜 can be explicitly described; and that the finite amount of information needed to construct it is computable.

How to cite

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McCord, Christopher. "Reconstructing the global dynamics of attractors via the Conley index." Banach Center Publications 47.1 (1999): 145-156. <http://eudml.org/doc/208930>.

@article{McCord1999,
abstract = {Given an unknown attractor 𝓐 in a continuous dynamical system, how can we discover the topology and dynamics of 𝓐? As a practical matter, how can we do so from only a finite amount of information? One way of doing so is to produce a semi-conjugacy from 𝓐 onto a model system 𝓜 whose topology and dynamics are known. The complexity of 𝓜 then provides a lower bound for the complexity of 𝓐. The Conley index can be used to construct a simplicial model and a surjective semi-conjugacy for a large class of attractors. The essential features of this construction are that the model 𝓜 can be explicitly described; and that the finite amount of information needed to construct it is computable.},
author = {McCord, Christopher},
journal = {Banach Center Publications},
keywords = {Conley index; semi-conjugacy; simplicial complex; attractor; continuous dynamical system; semiconjugacy},
language = {eng},
number = {1},
pages = {145-156},
title = {Reconstructing the global dynamics of attractors via the Conley index},
url = {http://eudml.org/doc/208930},
volume = {47},
year = {1999},
}

TY - JOUR
AU - McCord, Christopher
TI - Reconstructing the global dynamics of attractors via the Conley index
JO - Banach Center Publications
PY - 1999
VL - 47
IS - 1
SP - 145
EP - 156
AB - Given an unknown attractor 𝓐 in a continuous dynamical system, how can we discover the topology and dynamics of 𝓐? As a practical matter, how can we do so from only a finite amount of information? One way of doing so is to produce a semi-conjugacy from 𝓐 onto a model system 𝓜 whose topology and dynamics are known. The complexity of 𝓜 then provides a lower bound for the complexity of 𝓐. The Conley index can be used to construct a simplicial model and a surjective semi-conjugacy for a large class of attractors. The essential features of this construction are that the model 𝓜 can be explicitly described; and that the finite amount of information needed to construct it is computable.
LA - eng
KW - Conley index; semi-conjugacy; simplicial complex; attractor; continuous dynamical system; semiconjugacy
UR - http://eudml.org/doc/208930
ER -

References

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