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Pis'ma v Zh. Èksper. Teoret. Fiz., 2020, Volume 112, Issue 6, Pages 394–400 (Mi jetpl6262)  

NONLINEAR DYNAMICS

Lyapunov exponent for Whitney's problem with random drive

N. A. Stepanovabc, M. A. Skvortsovac

a Landau Institute for Theoretical Physics, Russian Academy of Sciences, Chernogolovka, Moscow region, 142432 Russia
b National Research University Higher School of Economics, Moscow, 101000 Russia
c Skolkovo Institute of Science and Technology, Moscow, 121205 Russia

Abstract: We consider the statistical properties of a non-falling trajectory in the Whitney problem of an inverted pendulum excited by an external force. In the case where the external force is white noise, we recently found the instantaneous distribution function of the pendulum angle and velocity over an infinite time interval using a transfer-matrix analysis of the supersymmetric field theory. Here, we generalize our approach to the case of finite time intervals and multipoint correlation functions. Using the developed formalism, we calculate the Lyapunov exponent, which determines the decay rate of correlations on a non-falling trajectory.

Funding Agency Grant Number
Russian Science Foundation 20-12-00361
This work was supported by the Russian Science Foundation (project no. 20-12-00361).


DOI: https://doi.org/10.31857/S1234567820180093

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English version:
Journal of Experimental and Theoretical Physics Letters, 2020, 112:6, 376–382

Bibliographic databases:

Received: 20.08.2020
Revised: 20.08.2020
Accepted:20.08.2020

Citation: N. A. Stepanov, M. A. Skvortsov, “Lyapunov exponent for Whitney's problem with random drive”, Pis'ma v Zh. Èksper. Teoret. Fiz., 112:6 (2020), 394–400; JETP Letters, 112:6 (2020), 376–382

Citation in format AMSBIB
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\paper Lyapunov exponent for Whitney's problem with random drive
\jour Pis'ma v Zh. \`Eksper. Teoret. Fiz.
\yr 2020
\vol 112
\issue 6
\pages 394--400
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\crossref{https://doi.org/10.31857/S1234567820180093}
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\jour JETP Letters
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\vol 112
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\pages 376--382
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