Generalized Lyapunov exponents of the random harmonic oscillator: Cumulant expansion approach

Physical Review E ◽

10.1103/physreve.85.021124 ◽

2012 ◽

Vol 85 (2) ◽

Cited By ~ 6

Author(s):

Raúl O. Vallejos ◽

Celia Anteneodo

Keyword(s):

Harmonic Oscillator ◽

Lyapunov Exponents ◽

Cumulant Expansion ◽

Generalized Lyapunov Exponents

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Generalized Lyapunov Exponents of Homogeneous Systems

2019 IEEE 58th Conference on Decision and Control (CDC) ◽

10.1109/cdc40024.2019.9029858 ◽

2019 ◽

Author(s):

Andrey Polyakov ◽

Sergiy Zhuk

Keyword(s):

Lyapunov Exponents ◽

Homogeneous Systems ◽

Generalized Lyapunov Exponents

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Anomalous scaling and generalized Lyapunov exponents of the one-dimensional Anderson model

Physical Review B ◽

10.1103/physrevb.35.2015 ◽

1987 ◽

Vol 35 (4) ◽

pp. 2015-2020 ◽

Cited By ~ 41

Author(s):

Giovanni Paladin ◽

Angelo Vulpiani

Keyword(s):

Lyapunov Exponents ◽

Anderson Model ◽

Anomalous Scaling ◽

One Dimensional ◽

The One ◽

Generalized Lyapunov Exponents

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Generalized Lyapunov exponents for products of correlated random matrices

Physical Review E ◽

10.1103/physreve.53.2960 ◽

1996 ◽

Vol 53 (3) ◽

pp. 2960-2963 ◽

Cited By ~ 19

Author(s):

M. J. de Oliveira ◽

A. Petri

Keyword(s):

Lyapunov Exponents ◽

Random Matrices ◽

Generalized Lyapunov Exponents

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Some formulas for Lyapunov exponents and rotation numbers in two dimensions and the stability of the harmonic oscillator and the inverted pendulum

Dynamical Systems ◽

10.1080/02681110010001289 ◽

2001 ◽

Vol 16 (1) ◽

pp. 29-61 ◽

Cited By ~ 14

Author(s):

Peter Imkeller ◽

Christian Lederer

Keyword(s):

Harmonic Oscillator ◽

Lyapunov Exponents ◽

Inverted Pendulum ◽

Two Dimensions ◽

Rotation Numbers ◽

The Stability

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Generalized Lyapunov exponents corresponding to higher derivatives

Physica D Nonlinear Phenomena ◽

10.1016/0167-2789(92)90076-y ◽

1992 ◽

Vol 59 (4) ◽

pp. 365-377 ◽

Cited By ~ 11

Author(s):

Ute Dressler ◽

J.Doyne Farmer

Keyword(s):

Lyapunov Exponents ◽

Higher Derivatives ◽

Generalized Lyapunov Exponents

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On generalized Lyapunov exponents

2011 19th Mediterranean Conference on Control & Automation (MED) ◽

10.1109/med.2011.5982994 ◽

2011 ◽

Cited By ~ 5

Author(s):

Adam Czornik ◽

Aleksander Nawrat

Keyword(s):

Lyapunov Exponents ◽

Generalized Lyapunov Exponents

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Estimating generalized Lyapunov exponents for products of random matrices

Physical Review E ◽

10.1103/physreve.81.036701 ◽

2010 ◽

Vol 81 (3) ◽

Cited By ~ 18

Author(s):

J. Vanneste

Keyword(s):

Lyapunov Exponents ◽

Random Matrices ◽

Products Of Random Matrices ◽

Generalized Lyapunov Exponents

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Generalized Lyapunov exponents in high-dimensional chaotic dynamics and products of large random matrices

Journal of Statistical Physics ◽

10.1007/bf01014215 ◽

1988 ◽

Vol 53 (3-4) ◽

pp. 583-601 ◽

Cited By ~ 17

Author(s):

Andrea Crisanti ◽

Giovanni Paladin ◽

Angelo Vulpiani

Keyword(s):

Lyapunov Exponents ◽

Random Matrices ◽

Chaotic Dynamics ◽

High Dimensional ◽

Generalized Lyapunov Exponents

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Characteristic and generalized Lyapunov exponents

Dynamical Systems Approach to Turbulence ◽

10.1017/cbo9780511599972.015 ◽

1998 ◽

pp. 301-308

Keyword(s):

Lyapunov Exponents ◽

Generalized Lyapunov Exponents

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Determining Zero Lyapunov Exponents in Continuous Time Dynamical Systems

International Journal of Modern Physics A ◽

10.1142/s0217751x97000165 ◽

1997 ◽

Vol 12 (01) ◽

pp. 131-135

Author(s):

İnanç Birol ◽

Avadis Hacinliyan

Keyword(s):

Dynamical Systems ◽

Nonlinear Systems ◽

Harmonic Oscillator ◽

Lyapunov Exponents ◽

Continuous Time ◽

Tangent Bundle ◽

Simple Harmonic Oscillator

Using the tangent bundle conjecture for the Lyapunov exponents, which considers these quantities as a generalization of eigenvalues to nonlinear systems, this work tries to identify zero exponents of a given system, if it exhibits one, via algebraic techniques. The existence of zero Lyapunov exponents for the Toda, Hénon-Heiles and two decoupled simple harmonic oscillator systems are shown.

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