# Reconstructing the global dynamics of attractors via the Conley index

Banach Center Publications (1999)

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

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topMcCord, 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 -

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