Lyapunov Exponent for Whitney's Problem with Random Drive
Abstract
We consider the statistical properties of a nonfalling 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 transfermatrix 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 nonfalling trajectory.
 Publication:

Soviet Journal of Experimental and Theoretical Physics Letters
 Pub Date:
 September 2020
 DOI:
 10.1134/S0021364020180034
 arXiv:
 arXiv:2008.12013
 Bibcode:
 2020JETPL.112..376S
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks;
 Mathematical Physics;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 6 pages, 3 figures