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The energy and the two partial energies of two-dimensional anisotropic harmonic oscillator are conserved quantities, but only two of them are independent. The system possesses the third independent conserved quantity when the 1/2 is a rational number. The extended Prelle-Singer method is used to find the third independent conserved quantity for the five typical two-dimensional anisotropic harmonic oscillators. The Noether symmetry and the Lie symmetry of the third independent conserved quantities are also discussed.
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Keywords:
- extended P-S method/
- two-dimensional anisotropic harmonic oscillator/
- conserved quantity/
- symmetry
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