Non-Archimedean normal families

We present several results on the compactness of space morphisms between analytic spaces in sense Berkovich. show that under certain conditions source, every sequence maps having an affinoid target has a subsequence converges pointwise to continuous map. also study class arise this way. Locally, they turn be after base change. Our naturally lead definition normal families. give some applications dynamics endomorphism projective space. introduce two natural notions Fatou set and generalize non-Archimedan setting theorem Ueda stating component is hyperbolically imbedded