Asymptotic Analysis of the Lyapunov Exponent and Rotation Number of the Random Oscillator and Applications

Ludwig Arnold; George Papanicolaou; Volker Wihstutz

doi:10.1137/0146030

Asymptotic Analysis of the Lyapunov Exponent and Rotation Number of the Random Oscillator and Applications

SIAM Journal on Applied Mathematics ◽

10.1137/0146030 ◽

1986 ◽

Vol 46 (3) ◽

pp. 427-450 ◽

Cited By ~ 118

Author(s):

Ludwig Arnold ◽

George Papanicolaou ◽

Volker Wihstutz

Keyword(s):

Lyapunov Exponent ◽

Asymptotic Analysis ◽

Rotation Number

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Asymptotic analysis for non-local curvature flows for plane curves with a general rotation number

Mathematics in Engineering ◽

10.3934/mine.2021047 ◽

2021 ◽

Vol 3 (6) ◽

pp. 1-26

Author(s):

Takeyuki Nagasawa ◽

◽

Kohei Nakamura

Keyword(s):

Asymptotic Analysis ◽

Rotation Number ◽

Plane Curves ◽

Local Curvature ◽

General Rotation ◽

Non Local

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Lyapunov exponent and rotation number of a two-dimensional nilpotent stochastic system

Dynamics and Stability of Systems ◽

10.1080/02681119008806079 ◽

1990 ◽

Vol 5 (1) ◽

pp. 1-9 ◽

Cited By ~ 14

Author(s):

S. T. Ariaratnam ◽

Wei Chau Xie

Keyword(s):

Lyapunov Exponent ◽

Rotation Number ◽

Stochastic System ◽

Two Dimensional

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Lyapunov exponent and rotation number for stochastic Dirac operators

Acta Mathematicae Applicatae Sinica English Series ◽

10.1007/bf02006742 ◽

1992 ◽

Vol 8 (4) ◽

pp. 333-347 ◽

Cited By ~ 1

Author(s):

Fengzhu Sun ◽

Minping Qian

Keyword(s):

Lyapunov Exponent ◽

Rotation Number ◽

Dirac Operators

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Maximal Lyapunov Exponent and Rotation Number for Stochastically Perturbed Co-dimension Two Bifurcations

Journal of Sound and Vibration ◽

10.1006/jsvi.1994.1022 ◽

1994 ◽

Vol 169 (3) ◽

pp. 349-372 ◽

Cited By ~ 14

Author(s):

N. Sri Namachchivaya ◽

S. Talwar

Keyword(s):

Lyapunov Exponent ◽

Rotation Number ◽

Maximal Lyapunov Exponent ◽

Stochastically Perturbed

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Asymptotic expansion of the Lyapunov exponent and the rotation number for the schrödinger operator with random potential

Lecture Notes in Control and Information Sciences - Stochastic Differential Systems Filtering and Control ◽

10.1007/bfb0005066 ◽

2005 ◽

pp. 113-120

Author(s):

Volker Wihstutz

Keyword(s):

Asymptotic Expansion ◽

Lyapunov Exponent ◽

Rotation Number ◽

Schrödinger Operator ◽

Random Potential ◽

Schrodinger Operator

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Lyapunov Exponent and Rotation Number of the Stochastic Harmonic Oscillator

The IMA Volumes in Mathematics and Its Applications - Random Media ◽

10.1007/978-1-4613-8725-1_16 ◽

1987 ◽

pp. 229-243

Author(s):

Mark A. Pinsky

Keyword(s):

Lyapunov Exponent ◽

Harmonic Oscillator ◽

Rotation Number

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Lyapunov exponent and rotation number of the linear harmonic oscillator

Diffusion Processes and Related Problems in Analysis, Volume II ◽

10.1007/978-1-4612-0389-6_11 ◽

1992 ◽

pp. 257-267 ◽

Cited By ~ 2

Author(s):

Mark A. Pinsky

Keyword(s):

Lyapunov Exponent ◽

Harmonic Oscillator ◽

Rotation Number ◽

Linear Harmonic Oscillator

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Reducible Linear Quasi-periodic Systems with Positive Lyapunov Exponent and Varying Rotation Number

Journal of Differential Equations ◽

10.1006/jdeq.2000.3877 ◽

2000 ◽

Vol 168 (1) ◽

pp. 60-66

Author(s):

H.W Broer ◽

C Simó

Keyword(s):

Lyapunov Exponent ◽

Rotation Number ◽

Positive Lyapunov Exponent ◽

Periodic Systems

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Lyapunov Exponent and Rotation Number of Two-Dimensional Linear Stochastic Systems with Small Diffusion

SIAM Journal on Applied Mathematics ◽

10.1137/0148024 ◽

1988 ◽

Vol 48 (2) ◽

pp. 442-457 ◽

Cited By ~ 72

Author(s):

E. Pardoux ◽

V. Wihstutz

Keyword(s):

Lyapunov Exponent ◽

Rotation Number ◽

Stochastic Systems ◽

Two Dimensional ◽

Small Diffusion ◽

Linear Stochastic Systems

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Lyapunov Exponent and Rotation Number of Two-Dimensional Linear Stochastic Systems with Telegraphic Noise

SIAM Journal on Applied Mathematics ◽

10.1137/0153017 ◽

1993 ◽

Vol 53 (1) ◽

pp. 283-300 ◽

Cited By ~ 2

Author(s):

Kenneth A. Loparo ◽

Xiangbo Feng

Keyword(s):

Lyapunov Exponent ◽

Rotation Number ◽

Stochastic Systems ◽

Two Dimensional ◽

Linear Stochastic Systems

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