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Pis'ma v Zhurnal Èksperimental'noi i Teoreticheskoi Fiziki, 2020, Volume 112, Issue 6, Pages 394–400
DOI: https://doi.org/10.31857/S1234567820180093 (Mi jetpl6262) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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
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DOI: https://doi.org/10.31857/S1234567820180093
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).
Received: 20.08.2020
Revised: 20.08.2020
Accepted: 20.08.2020
English version:
Journal of Experimental and Theoretical Physics Letters, 2020, Volume 112, Issue 6, Pages 376–382
DOI: https://doi.org/10.1134/S0021364020180034
Bibliographic databases:
Document Type: Article
Language: Russian
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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\pages 394--400
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\jour JETP Letters
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\pages 376--382
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  • https://www.mathnet.ru/eng/jetpl6262
  • https://www.mathnet.ru/eng/jetpl/v112/i6/p394
    • This publication is cited in the following 1 articles:
    1. Nikolay Stepanov, Mikhail Skvortsov, SciPost Phys., 13:2 (2022)  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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