For the integrability of the 2D trapped ionic system.

In this paper we will explore the 2D system with Hamiltonian H = 1 2 (p r 2 + p z 2) + A r 2 + B z 2 + C z 3 + D r 2 z + E z 4 + F r 2 z 2 + G r 4 , describing trapped ionic system in the quadrapole field with a superposition of rationally symmetric hexapole and octopole fields for meromorphic integrability. We use the Lyapunov and Ziglin-Morales-Ruiz-Ramis's classical methods for the proofs. [ABSTRACT FROM AUTHOR]