Variational principle for neutralized packing pressure on subsets
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914126800879616 |
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| author | Xiao, Zubiao Jia, Hongwei |
| author_facet | Xiao, Zubiao Jia, Hongwei |
| contents | 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 $\overline{P}_{μ,{\mathcal{G}} }(Z,f)$ for a given continuous function $f$ and a compact subset $Z \subset X$:
$$P^{P}_{\mathcal{G}}(Z,f)=\lim_{\varepsilon \to 0}\sup \{ \overline{P}_{μ,\mathcal{G} }(Z,f,\varepsilon):μ\in M(X), \ μ(Z)=1 \}.$$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27221 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variational principle for neutralized packing pressure on subsets Xiao, Zubiao Jia, Hongwei Dynamical Systems 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 $\overline{P}_{μ,{\mathcal{G}} }(Z,f)$ for a given continuous function $f$ and a compact subset $Z \subset X$: $$P^{P}_{\mathcal{G}}(Z,f)=\lim_{\varepsilon \to 0}\sup \{ \overline{P}_{μ,\mathcal{G} }(Z,f,\varepsilon):μ\in M(X), \ μ(Z)=1 \}.$$ |
| title | Variational principle for neutralized packing pressure on subsets |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2510.27221 |