Variational principle for neutralized packing pressure on subsets

Zubiao Xiao; Hongwei Jia

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arXiv · 2510.27221

Variational principle for neutralized packing pressure on subsets

Zubiao Xiao·Hongwei Jia

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Abstract

In this paper, we introduce the notions of neutralized packing pressures and neutralized measure-theoretic pressures on subsets for a finitely generated free semigroup action. Let $X$ be a compact metric space and $\mathcal{G}$ be a finite family of continuous self-maps on $X$. We consider the semigroup $G$ generated by $\mathcal{G}$ on $X$. We show that the variational principle between the neutralized packing pressures $P^{P}_{\mathcal{G}}(Z,f)$ and the neutralized measure--theoretic upper pressures $\overline{P}_{\mu,{\mathcal{G}} }(Z,f)$ for a given continuous function $f$ and a compact subset $Z \subset X$: $$P^{P}_{\mathcal{G}}(Z,f)=\lim_{\varepsilon \to 0}\sup \{ \overline{P}_{\mu,\mathcal{G} }(Z,f,\varepsilon):\mu \in M(X), \ \mu(Z)=1 \}.$$

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Zubiao Xiao, Hongwei Jia. 2025-10-31. Variational principle for neutralized packing pressure on subsets. https://arxiv.org/abs/2510.27221

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