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<p>In this paper, we investigate the variational principle for neutralized topological pressure on subsets under amenable group actions. Extending the classical notion from <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {Z}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">Z</mi> </math></EquationSource> </InlineEquation>-actions, we introduce the neutralized Pesin–Pitskel topological pressure for arbitrary subsets, defined via Bowen balls with exponentially shrinking radii. We introduce two measure-theoretic analogues: the lower neutralized Brin–Katok local pressure and the neutralized Katok pressure. By employing the Carathéodory dimension structure, we establish a Billingsley-type theorem and derive a variational principle applicable to compact subsets.</p>

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Variational Principle for Neutralized Topological Pressure on Subsets under Amenable Group Actions

  • 期刊论文

  • 发表日期：

    2026年4月17日

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  • Lei Liu,
  • Dongmei Peng

摘要

In this paper, we investigate the variational principle for neutralized topological pressure on subsets under amenable group actions. Extending the classical notion from \(\mathbb {Z}\) Z -actions, we introduce the neutralized Pesin–Pitskel topological pressure for arbitrary subsets, defined via Bowen balls with exponentially shrinking radii. We introduce two measure-theoretic analogues: the lower neutralized Brin–Katok local pressure and the neutralized Katok pressure. By employing the Carathéodory dimension structure, we establish a Billingsley-type theorem and derive a variational principle applicable to compact subsets.