Variational aspect and kinetic theory of locally conformal dynamics

Abstract

We present the locally conformal generalization of the Euler-Lagrange equations. We determine the dual space of the LCS Hamiltonian vector fields. Within this dual space, we formulate the Lie-Poisson equation that governs the kinetic motion of Hamiltonian systems in the context of local conformality. By expressing the Lie-Poisson dynamics in terms of density functions, we derive locally conformal Vlasov dynamics. In addition, we outline a geometric pathway that connects LCS Hamiltonian particle motion to locally conformal kinetic motion.