Abstract
In this paper, the Lyapunov exponent and rotation number of a family of two-dimensional systems with general telegraphic noise where the unperturbed system has oscillatory behavior are studied. Using a martingale approach, an iterative computational procedure is derived and analytic expansions in the noise strength are obtained for the Lyapunov exponent and the rotation number. These expansions are convergent in a nonmarginal way. The positivity of the exponent is also established for the random harmonic oscillator with zero-mean telegraphic noise, and lower and upper bounds are derived for the exponent when the noise is the random telegraph process.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
