Conformal invariance and conserved quantities of Hamilton system under second-class Mei symmetry are studied. The single-parameter infinitesimal transformation group and infinitesimal transformation vector of generator are introduced. The definitions about conformal invariance of Hamilton function and conformal invariance of Hamilton system under second-class Mei symmetry are given. The relationship between the system's conformal invariance and Mei symmetry are discussed. The necessary and sufficient condition that the system's conformal invariance would be Mei symmetry is deduced. The system's corresponding conserved quantities are obtained with the aid of a structure equation which is satisfied by the gauge function. Lastly, an example is provided to illustrate the application of the result.

Conformal invariance and conserved quantities of the Mei symmetry for the Lagrange systems under the infinitesimal transformation of groups are studied. Firstly, the definition of conformal invariance of the Mei symmetry is given, together with its criterion equations and determining equations. Then the systems' conserved quantities are obtained using the structure equation satisfied by the gauge function. Lastly, an example is taken to illustrate the application of the result.

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In this paper, the conformal invariance and conserved quantities for higher-order holonomic systems are studied. Firstly, by establishing the differential equation of motion for the systems and introducing a one-parameter infinitesimal transformation group together with its infinitesimal generator vector, the determining equation of conformal invariance for the systems are provided, and the conformal factors expression are deduced. Secondly, the relation between conformal invariance and the Lie symmetry by the infinitesimal one-parameter point transformation group for the higher-order holonomic systems are deduced. Thirdly, the conserved quantities of the systems are derived using the structure equation satisfied by the gauge function. Lastly, an example of a higher-order holonomic mechanical system is discussed to illustrate these results.