Basic theory of fractional Mei symmetrical perturbation and its applications

摘要: In this paper, we present a new method of fractional dynamics, i.e., the Mei symmetrical perturbation disturbed system, and explore adiabatic invariant directly led by perturbation. For dynamical system which is small forces perturbation, generalized Hamiltonian equation investigated and, under more general kind infinitesimal transformation Lie group, definition determining are given; then, obtained. particular, it found that, using method, can find non-Noether As special cases, obtain conservation law undisturbed theorem integer system. Also, as method’s applications, invariants Duffing oscillator Lotka biochemical oscillator. This work constructs basic theoretical framework provides dynamics.