Upper metric mean dimensions with potential on subsets. (English) Zbl 1457.49026
Summary: In this paper, we introduce the notion of upper metric mean dimension with potential on any subset (not necessarily compact or invariant) via Carathéodory-Pesin structures. We discuss several possible versions of upper measure-theoretic mean dimensions with potential and find conditions to make these notions coincide. In particular, we present a corresponding variational principle and an inverse variational principle.
MSC:
| 49N45 | Inverse problems in optimal control |
References:
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