The Hamiltonian Formulation of Higher Order Dynamical Systems

Using Dirac's approach to constrained dynamics, the Hamiltonian formulation of regular higher order Lagrangians is developed. The conventional description of such systems due to Ostrogradsky is recovered. However, unlike the latter, the present analysis yields in a transparent manner the local structure of the associated phase space and its local sympletic geometry, and is of direct application to {\em constrained\/} higher order Lagrangian systems which are beyond the scope of Ostrogradsky's approach.Comment: 17 pages. Revised: references adde

On Strong Small Loop Transfer Spaces Relative to Subgroups of Fundamental Groups

Let $H$ be a subgroup of the fundamental group $\pi_{1}(X,x_{0})$. By extending the concept of strong SLT space to a relative version with respect to $H$, strong $H$-SLT space, first, we investigate the existence of a covering map for strong $H$-SLT spaces. Moreover, we show that a semicovering map is a covering map in the presence of strong $H$-SLT property. Second, we present conditions under which the whisker topology agrees with the lasso topology on $\widetilde{X}_{H}$. Also, we study the relationship between open subsets of $\pi_{1}^{wh}(X,x_{0})$ and $\pi_{1}^{l}(X,x_{0})$. Finally, we give some examples to justify the definition and study of strong $H$-SLT spaces.Comment: 16 page