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In this paper, unstable metric entropy, unstable topological entropy andunstable pressure for partially hyperbolic endomorphisms are introduced andinvestigated. A version of Shannon-McMillan-Breiman Theorem is established, anda variational principle is formulated, which gives a relationship betweenunstable metric entropy and unstable pressure (unstable topological entropy).As an application of the variational principle, some results on the$u$-equilibrium states are given.

Unstable Entropy and Unstable Pressure for Partially Hyperbolic Endomorphisms