Exponential Growth Rates of Periodic Asymmetric Oscillators
نویسندگان
چکیده
In this paper we will study the dynamics of the periodic asymmetric oscillator x′′ + q(t)x+ + q−(t)x− = 0, where q, q− ∈ L(R/2πZ) and x+ = max(x, 0), x− = min(x, 0) for x ∈ R. It will be proved that the exponential growth rate χ(x) := lim t→+∞ 1 t log √ (x(t))2 + (x′(t))2 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 diffeomorphism of the oscillator. The proof is extensively based on the Denjoy theorem in topological dynamics and the unique ergodicity theorem in ergodic theory. 2000 Mathematics Subject Classification. Primary: 34D08; Secondary: 37E10, 37A25.
منابع مشابه
Dynamic Systems and Applications 19 (2010) 147-164 CLASSIFICATION OF SOLUTIONS OF ASYMMETRIC p-LAPLACIAN OSCILLATORS WITH PERIODIC COEFFICIENTS
By exploiting the Denjoy theorem in topological dynamics and the unique ergodic theorem in ergodic theory, we will give a classification of all solutions of asymmetric p-Laplacian oscillators with periodic coefficients. AMS (MOS) Subject Classification. Primary: 34D08; Secondary: 37E10, 37A25.
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