| Contents |
| We present a proof of a normally hyperbolic invariant manifold theorem
for maps. The proof is conducted in the phase space of the system.
The result is not perturbative. We give explicit conditions under which
the existence and smoothness of a normally hyperbolic invariant manifold,
together with its associated stable and unstable manifolds, is ensured inside
of a given explicit bound. The assumptions are based on estimates
on the map and on estimates of its derivative. Assumptions are formulated
in a way, which allows for rigorous, interval-based, computer assisted
verification. |
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