Conformal Newton-Hooke algebras, Niederer's transformation and Pais-Uhlenbeck oscillator

Dynamical systems invariant under the action of the l-conformal Newton-Hooke algebras are constructed by the method of nonlinear realizations. The relevant first order Lagrangians together with the corresponding Hamiltonians are found. The relation to the Galajinsky and Masterov [24] approach as well as the higher derivatives formulation is discussed. The generalized Niederer's transformation ispresented which relatesthe systems under consideration to those invariant under the action of the l-conformal Galilei algebra [25]. As a nice application of these results an analogue of Niederer's transformation, on the Hamiltonian level, for the Pais-Uhlenbeck oscillator is constructed. (C) 2014 The Author. Published by Elsevier B. V. This is an open access article under the CC BY license (http://creativecommons. org/licenses/by/3.0/). Funded by SCOAP(3).