Accessible Unlicensed Requires Authentication Published by De Gruyter March 10, 2016

Exponential Growth Rates of Periodic Asymmetric Oscillators

Meirong Zhang and Zhe Zhou


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.

Published Online: 2016-3-10
Published in Print: 2008-11-1

© 2016 by Advanced Nonlinear Studies, Inc.