Abstract
Abstract In this paper we will study the dynamics of the periodic asymmetric oscillator xʺ + q+(t)x+ + q–(t)x– = 0, where q+; q– ∊ L1(ℝ / 2πℤ) and x+ = max(x; 0), x– = min(x; 0) for x ∊ ℝ. It will be proved that the exponential growth rate does exist for each non-zero solution x(t) of the oscillator. The properties of these rates, or the Lyapunov exponents, will be given using the induced circle di®eomorphism of the oscillator. The proof is extensively based on the Denjoy theorem in topological dynamics and the unique ergodicity theorem in ergodic theory.
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.
