  Shortcomings of Dirac's constrained analysis in the context of fourth order
Pais-Uhlenbeck oscillator action and the appearance of badly affected
phase-space Hamiltonian for a generalized fourth order oscillator action,
following Ostrogradski, Dirac and Horowitz's formalism, require a viable
canonical formulation. This is achieved only after fixing appropriate variables
at the end points and taking care of the counter surface terms obtained from
variational principle. In the process a one-to-one correspondence between
different higher order theories has been established. On the other hand the
issue of branched Hamiltonian appearing in the presence of velocities with
degree higher than two in the Lagrangian, has not been resolved uniquely as
yet. However, often such terms appear with higher order theory, gravity in
particular. Here we show that canonical formulation of higher order theory
takes care of the issue elegantly.
