Imperial College London
Professor Dmitry Turaev

ProfessorDmitryTuraev

Faculty of Natural Sciences, Department of Mathematics

Professor of Applied Mathematics & Mathematical Physics
 
 
 
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Contact

 

d.turaev

 
 
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Location

 

634Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Capiński:2018:1361-6544/aae032,
author = {Capiski, MJ and Turaev, D and Zgliczyski, P},
doi = {1361-6544/aae032},
journal = {Nonlinearity},
pages = {5410--5440},
title = {Computer assisted proof of the existence of the Lorenz attractor in the Shimizu–Morioka system},
url = {http://dx.doi.org/10.1088/1361-6544/aae032},
volume = {31},
year = {2018}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We prove that the Shimizu–Morioka system has a Lorenz attractor for an open set of parameter values. For the proof we employ a criterion proposed by Shilnikov, which allows to conclude the existence of the attractor by examination of the behaviour of only one orbit. The needed properties of the orbit are established by using computer assisted numerics. Our result is also applied to the study of local bifurcations of triply degenerate periodic points of three-dimensional maps. It provides a formal proof of the birth of discrete Lorenz attractors at various global bifurcations.
AU  - Capiski,MJ
AU  - Turaev,D
AU  - Zgliczyski,P
DO  - 1361-6544/aae032
EP  - 5440
PY  - 2018///
SN  - 0951-7715
SP  - 5410
TI  - Computer assisted proof of the existence of the Lorenz attractor in the Shimizu–Morioka system
T2  - Nonlinearity
UR  - http://dx.doi.org/10.1088/1361-6544/aae032
UR  - http://hdl.handle.net/10044/1/64436
VL  - 31
ER  -
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