Abstract
This paper contributes to the mean dimension theory of dynamical systems. We introduce a new concept called mean dimension with potential and develop a variational principle for it. This is a mean dimension analogue of the theory of topological pressure. We consider a minimax problem for the sum of rate distortion dimension and the integral of a potential function. We prove that the minimax value is equal to the mean dimension with potential for a dynamical system having the marker property. The basic idea of the proof is a dynamicalization of geometric measure theory.
| Original language | English |
|---|---|
| Article number | 106935 |
| Journal | Advances in Mathematics |
| Volume | 361 |
| DOIs | |
| Publication status | Published - Feb 12 2020 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
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Double variational principle for mean dimension with potential. / Tsukamoto, Masaki.
In: Advances in Mathematics, Vol. 361, 106935, 12.02.2020.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Double variational principle for mean dimension with potential
AU - Tsukamoto, Masaki
PY - 2020/2/12
Y1 - 2020/2/12
N2 - This paper contributes to the mean dimension theory of dynamical systems. We introduce a new concept called mean dimension with potential and develop a variational principle for it. This is a mean dimension analogue of the theory of topological pressure. We consider a minimax problem for the sum of rate distortion dimension and the integral of a potential function. We prove that the minimax value is equal to the mean dimension with potential for a dynamical system having the marker property. The basic idea of the proof is a dynamicalization of geometric measure theory.
AB - This paper contributes to the mean dimension theory of dynamical systems. We introduce a new concept called mean dimension with potential and develop a variational principle for it. This is a mean dimension analogue of the theory of topological pressure. We consider a minimax problem for the sum of rate distortion dimension and the integral of a potential function. We prove that the minimax value is equal to the mean dimension with potential for a dynamical system having the marker property. The basic idea of the proof is a dynamicalization of geometric measure theory.
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UR - http://www.scopus.com/inward/citedby.url?scp=85076246086&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2019.106935
DO - 10.1016/j.aim.2019.106935
M3 - Article
AN - SCOPUS:85076246086
VL - 361
JO - Advances in Mathematics
JF - Advances in Mathematics
SN - 0001-8708
M1 - 106935
ER -