Abstract
In this paper we introduce the Pesin-Pitskel unstable pressure to study dynamical complexity of general subsets in partially hyperbolic systems. We establish some basic results in dimension theory for Pesin-Pitskel unstable pressure, including a pressure distribution principle, and a variational principle for any compact (not necessarily invariant) subset between its Pesin-Pitskel unstable pressure and unstable metric pressure of probability measures supported on this set.
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