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Lyapunov dimension formula for the global attractor of the Lorenz system

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Leonov, G. A., Kuznetsov, N., Korzhemanova, N. A., & Kusakin, D. V. (2016). Lyapunov dimension formula for the global attractor of the Lorenz system. Communications in Nonlinear Science and Numerical Simulation, 41, 84-103. https://doi.org/10.1016/j.cnsns.2016.04.032
Published in
Communications in Nonlinear Science and Numerical Simulation
Authors
Leonov, G. A. |
Kuznetsov, Nikolay |
Korzhemanova, N. A. |
Kusakin, D. V.
Date
2016
Discipline
TietotekniikkaMathematical Information Technology
Copyright
© 2016 Elsevier B.V. This is a final draft version of an article whose final and definitive form has been published by Elsevier. Published in this repository with the kind permission of the publisher.

 
The exact Lyapunov dimension formula for the Lorenz system for a positive measure set of parameters, including classical values, was analytically obtained first by G.A. Leonov in 2002. Leonov used the construction technique of special Lyapunov-type functions, which was developed by him in 1991 year. Later it was shown that the consideration of larger class of Lyapunov-type functions permits proving the validity of this formula for all parameters, of the system, such that all the equilibria of the system are hyperbolically unstable. In the present work it is proved the validity of the formula for Lyapunov dimension for a wider variety of parameters values including all parameters, which satisfy the classical physical limitations.
Publisher
Elsevier B.V.; Peking University
ISSN Search the Publication Forum
1007-5704
Keywords
Lorenz system self-excited Lorenz attractor Kaplan-Yorke dimension Lyapunov dimension Lyapunov exponents
DOI
https://doi.org/10.1016/j.cnsns.2016.04.032
URI

http://urn.fi/URN:NBN:fi:jyu-201606062912

Publication in research information system

https://converis.jyu.fi/converis/portal/detail/Publication/25680557

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  • Informaatioteknologian tiedekunta [1967]

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