
TY  - JOUR
A1  - Steeb, W-H 
A1  - Louw, JA 
A1  - Villet, CM 
T1  - Linearly Coupled Anharmonic Oscillators and Integrability
JF  - Australian Journal of Physics
JO  - Aust. J.  Phys.
Y1  - 1987
VL  - 40
IS  - 5
SP  - 587
EP  - 592
KW  - 
UR  - https://doi.org/10.1071/PH870587 
N2  - The Painleve test for a linearly coupled anharmonic oscillator is performed. We show that this system does not pass the Painleve test. This suggests that this system is not integrable. Moreover, we apply Ziglin's (1983) theorem which provides a criterion for non-existence of first integrals besides the Hamiltonian. Calculating numerically the maximal one-dimensional Lyapunov exponent, we find regions with positive exponents. Thus, the system can show chaotic behaviour. Finally we compare our results with the quartic coupled anharmonic oscillator. 
ER  -

