On the existence of higher order Lyapunov exponents

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The author proves the existence of an exponential rate of growth for the second derivative of a one-dimensional dynamical system with positive Lyapunov exponent, and prove that the second order Lyapunov exponent thus defined is equal to precisely twice the first order derivative. Similar techniques shed some light on the multidimensional case. This work extends results of Dressler and Farmer (1991) and verifies a conjecture of Farmer and Sidorowich (1987) related to a priori estimates for time series forecasting.

Original languageEnglish (US)
Article number002
Pages (from-to)369-375
Number of pages7
JournalNonlinearity
Volume6
Issue number3
DOIs
StatePublished - 1993

Fingerprint

Lyapunov Exponent
exponents
Higher Order
Derivatives
Time Series Forecasting
Second derivative
A Priori Estimates
forecasting
dynamical systems
Time series
Dynamical systems
Dynamical system
Verify
First-order
Derivative
estimates

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics
  • Applied Mathematics
  • Mathematics(all)

Cite this

On the existence of higher order Lyapunov exponents. / Taylor, Thomas.

In: Nonlinearity, Vol. 6, No. 3, 002, 1993, p. 369-375.

Research output: Contribution to journalArticle

@article{665b95ea89094957a7ae69dbade69439,
title = "On the existence of higher order Lyapunov exponents",
abstract = "The author proves the existence of an exponential rate of growth for the second derivative of a one-dimensional dynamical system with positive Lyapunov exponent, and prove that the second order Lyapunov exponent thus defined is equal to precisely twice the first order derivative. Similar techniques shed some light on the multidimensional case. This work extends results of Dressler and Farmer (1991) and verifies a conjecture of Farmer and Sidorowich (1987) related to a priori estimates for time series forecasting.",
author = "Thomas Taylor",
year = "1993",
doi = "10.1088/0951-7715/6/3/002",
language = "English (US)",
volume = "6",
pages = "369--375",
journal = "Nonlinearity",
issn = "0951-7715",
publisher = "IOP Publishing Ltd.",
number = "3",

}

TY - JOUR

T1 - On the existence of higher order Lyapunov exponents

AU - Taylor, Thomas

PY - 1993

Y1 - 1993

N2 - The author proves the existence of an exponential rate of growth for the second derivative of a one-dimensional dynamical system with positive Lyapunov exponent, and prove that the second order Lyapunov exponent thus defined is equal to precisely twice the first order derivative. Similar techniques shed some light on the multidimensional case. This work extends results of Dressler and Farmer (1991) and verifies a conjecture of Farmer and Sidorowich (1987) related to a priori estimates for time series forecasting.

AB - The author proves the existence of an exponential rate of growth for the second derivative of a one-dimensional dynamical system with positive Lyapunov exponent, and prove that the second order Lyapunov exponent thus defined is equal to precisely twice the first order derivative. Similar techniques shed some light on the multidimensional case. This work extends results of Dressler and Farmer (1991) and verifies a conjecture of Farmer and Sidorowich (1987) related to a priori estimates for time series forecasting.

UR - http://www.scopus.com/inward/record.url?scp=0000419998&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000419998&partnerID=8YFLogxK

U2 - 10.1088/0951-7715/6/3/002

DO - 10.1088/0951-7715/6/3/002

M3 - Article

VL - 6

SP - 369

EP - 375

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 3

M1 - 002

ER -