Symplectic Transversality and Endpoint Green Estimates for Finite-Horizon Pontryagin Systems

The paper presents a study on finite-horizon discrete-time Pontryagin boundary value systems, focusing on horizon-uniform local branches post smooth control elimination. It introduces a two-point endpoint inverse for the linearization, proving its validity through scaled stable-unstable boundary transversality and deriving an endpoint-corrected Green estimate, which ensures existence, uniqueness, and Lipschitz dependence of solutions. This framework is significant for practitioners as it encompasses smooth nonlinear endpoint maps and stabilizable linear-quadratic systems, providing a robust methodology for analyzing control systems with independent constants of expansion across varying horizons.