Rigorous lower bounds for the domains of definition of extended generating functions

The recently developed theory of extended generating functions of symplectic maps are combined with methods to prove invertibility via high-order Taylor model methods to obtain rigorous lower bounds for the domains of definition of generating functions. The examples presented suggest that there are considerable differences in the size of the domains of definition of the various types of generating functions studied. Furthermore, the types of generating functions for which, in general, large domains of definitions can be guarantied were identified. The resulting domain sizes of these generators are usually sufficiently large to be useful in practice, for example for the long-term simulations of accelerator and other Hamiltonian system dynamics.