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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
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.
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
Linking options:
https://www.mathnet.ru/eng/jetpl6262 https://www.mathnet.ru/eng/jetpl/v112/i6/p394
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Abstract page: | 115 | Full-text PDF : | 22 | References: | 26 | First page: | 5 |
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