| Abstract: |
| We investigate the Noether-type Hamiltonian symmetry classification, first integrals and exact solutions of Ermakov's system. We utilize the Hamiltonian version of Noether's theorem to construct Noether
symmetries and first integrals. The Ermakov's system involves an arbitrary function. First, Noether-type Hamiltonian symmetry classification is performed for the Ermakov's system. For the arbitrary form of function four first integrals are established and only three of these first integrals are functionally independent. The Hamiltonian version of Noether's theorem yields several different functional forms of arbitrary function for which the Ermakov's system has the additional Noether-type Hamiltonian symmetries and first integrals. Finally, the exact solutions of Ermakov's system are established with the aid of these derived first integrals. |
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