A Variational Principle for the Metric Mean Dimension of Level Sets
A Variational Principle for the Metric Mean Dimension of Level Sets
We prove a variational principle for the upper and lower metric mean dimension of level sets <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\left \{{x\in X: \lim _{n\to \infty }\frac {1}{n}\sum _{j=0}^{n-1}\varphi (f^{j}(x))=\alpha }\right \}$ </tex-math></inline-formula> associated to continuous potentials <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varphi:X\to \mathbb R$ </tex-math></inline-formula> and continuous dynamics <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" …