2 problems

Define the bounded-motion region … Here $E$ is the particle energy, $L$ its angular momentum, $V$ the effective potential, and $H$ the Hamiltonian. Generic Schwarzschild bounded-ph…

Let $N_\varepsilon$ denote the perturbed normally hyperbolic invariant manifold associated with the photon sphere, and let $L$ and $L_z$ be the angular-momentum quantities used in…