Standard

Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations. / Kuznetsov, N. V.; Alexeeva, T. A.; Leonov, G. A.

In: Nonlinear Dynamics, Vol. 85, No. 1, 01.07.2016, p. 195-201.

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

Harvard

Kuznetsov, NV, Alexeeva, TA & Leonov, GA 2016, 'Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations', Nonlinear Dynamics, vol. 85, no. 1, pp. 195-201. https://doi.org/10.1007/s11071-016-2678-4

APA

Kuznetsov, N. V., Alexeeva, T. A., & Leonov, G. A. (2016). Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations. Nonlinear Dynamics, 85(1), 195-201. https://doi.org/10.1007/s11071-016-2678-4

Vancouver

Kuznetsov NV, Alexeeva TA, Leonov GA. Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations. Nonlinear Dynamics. 2016 Jul 1;85(1):195-201. https://doi.org/10.1007/s11071-016-2678-4

Author

Kuznetsov, N. V. ; Alexeeva, T. A. ; Leonov, G. A. / Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations. In: Nonlinear Dynamics. 2016 ; Vol. 85, No. 1. pp. 195-201.

BibTeX

@article{faa7c40146e54505bd0856d5f7518765,
title = "Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations",
abstract = "Nowadays the Lyapunov exponents and Lyapunov dimension have become so widespread and common that they are often used without references to the rigorous definitions or pioneering works. It may lead to a confusion since there are at least two well-known definitions, which are used in computations: the upper bounds of the exponential growth rate of the norms of linearized system solutions (Lyapunov characteristic exponents, LCEs) and the upper bounds of the exponential growth rate of the singular values of the fundamental matrix of linearized system (Lyapunov exponents, LEs). In this work, the relation between Lyapunov exponents and Lyapunov characteristic exponents is discussed. The invariance of Lyapunov exponents for regular and irregular linearizations under the change of coordinates is demonstrated.",
keywords = "Diffeomorphism, Lyapunov characteristic exponent, Lyapunov dimension of attractor, Lyapunov exponent, Regular and irregular linearization, Time-varying linearization",
author = "Kuznetsov, {N. V.} and Alexeeva, {T. A.} and Leonov, {G. A.}",
year = "2016",
month = jul,
day = "1",
doi = "10.1007/s11071-016-2678-4",
language = "English",
volume = "85",
pages = "195--201",
journal = "Nonlinear Dynamics",
issn = "0924-090X",
publisher = "Springer Nature",
number = "1",

}

RIS

TY - JOUR

T1 - Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations

AU - Kuznetsov, N. V.

AU - Alexeeva, T. A.

AU - Leonov, G. A.

PY - 2016/7/1

Y1 - 2016/7/1

N2 - Nowadays the Lyapunov exponents and Lyapunov dimension have become so widespread and common that they are often used without references to the rigorous definitions or pioneering works. It may lead to a confusion since there are at least two well-known definitions, which are used in computations: the upper bounds of the exponential growth rate of the norms of linearized system solutions (Lyapunov characteristic exponents, LCEs) and the upper bounds of the exponential growth rate of the singular values of the fundamental matrix of linearized system (Lyapunov exponents, LEs). In this work, the relation between Lyapunov exponents and Lyapunov characteristic exponents is discussed. The invariance of Lyapunov exponents for regular and irregular linearizations under the change of coordinates is demonstrated.

AB - Nowadays the Lyapunov exponents and Lyapunov dimension have become so widespread and common that they are often used without references to the rigorous definitions or pioneering works. It may lead to a confusion since there are at least two well-known definitions, which are used in computations: the upper bounds of the exponential growth rate of the norms of linearized system solutions (Lyapunov characteristic exponents, LCEs) and the upper bounds of the exponential growth rate of the singular values of the fundamental matrix of linearized system (Lyapunov exponents, LEs). In this work, the relation between Lyapunov exponents and Lyapunov characteristic exponents is discussed. The invariance of Lyapunov exponents for regular and irregular linearizations under the change of coordinates is demonstrated.

KW - Diffeomorphism

KW - Lyapunov characteristic exponent

KW - Lyapunov dimension of attractor

KW - Lyapunov exponent

KW - Regular and irregular linearization

KW - Time-varying linearization

UR - http://www.scopus.com/inward/record.url?scp=84959374949&partnerID=8YFLogxK

U2 - 10.1007/s11071-016-2678-4

DO - 10.1007/s11071-016-2678-4

M3 - Article

AN - SCOPUS:84959374949

VL - 85

SP - 195

EP - 201

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 1

ER -

ID: 52007752