Lyapunov dimension formula for the global attractor of the Lorenz system

Standard

Lyapunov dimension formula for the global attractor of the Lorenz system. / Leonov, G. A.; Kuznetsov, N. V.; Korzhemanova, N. A.; Kusakin, D. V.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 41, 01.12.2016, p. 84-103.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{10eeee01bf3145c19014b59cbc1db07e,

title = "Lyapunov dimension formula for the global attractor of the Lorenz system",

abstract = "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.",

keywords = "Kaplan-Yorke dimension, Lorenz system, Lyapunov dimension, Lyapunov exponents, Self-excited Lorenz attractor",

author = "Leonov, {G. A.} and Kuznetsov, {N. V.} and Korzhemanova, {N. A.} and Kusakin, {D. V.}",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",

year = "2016",

month = dec,

day = "1",

doi = "10.1016/j.cnsns.2016.04.032",

language = "English",

volume = "41",

pages = "84--103",

journal = "Communications in Nonlinear Science and Numerical Simulation",

issn = "1007-5704",

publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Lyapunov dimension formula for the global attractor of the Lorenz system

AU - Leonov, G. A.

AU - Kuznetsov, N. V.

AU - Korzhemanova, N. A.

AU - Kusakin, D. V.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - 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.

AB - 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.

KW - Kaplan-Yorke dimension

KW - Lorenz system

KW - Lyapunov dimension

KW - Lyapunov exponents

KW - Self-excited Lorenz attractor

UR - http://www.scopus.com/inward/record.url?scp=84969764618&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2016.04.032

DO - 10.1016/j.cnsns.2016.04.032

M3 - Article

AN - SCOPUS:84969764618

VL - 41

SP - 84

EP - 103

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

ER -

ID: 95259474