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<p>In this paper, for a <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12346_2025_1390_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation> partially hyperbolic diffeomorphism <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12346_2025_1390_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="91" /> </InlineMediaObject> <EquationSource Format="TEX">\(f:M\rightarrow M\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo>:</mo> <mi>M</mi> <mo stretchy="false">→</mo> <mi>M</mi> </mrow> </math></EquationSource> </InlineEquation>, we introduce the concept of nonlinear unstable neutralized topological pressure on subsets, present the Billingsley-type theorem and subsequently establish a corresponding variational principle. This work is motivated by [Buzzi, Kloeckner, Leplaideur, Ann. H. Lebesgue <b>6</b>, 1429–1477 (2023), Ovadia, Rodríguez-Hertz, Int. Math. Res. Not. IMRN <b>11</b>, 9469–9481 (2024), Tian, Wu, Nonlinearity <b>35</b>(1), 658–680 (2022)].</p>

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Nonlinear Unstable Neutralized Pressure of Subsets for Partially Hyperbolic Systems

  • 期刊论文

  • 发表日期：

    2025年10月8日

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  • Zeya Mi,
  • Yiwen Zhang,
  • Congcong Qu

摘要

In this paper, for a \(C^1\) C 1 partially hyperbolic diffeomorphism \(f:M\rightarrow M\) f : M → M , we introduce the concept of nonlinear unstable neutralized topological pressure on subsets, present the Billingsley-type theorem and subsequently establish a corresponding variational principle. This work is motivated by [Buzzi, Kloeckner, Leplaideur, Ann. H. Lebesgue 6, 1429–1477 (2023), Ovadia, Rodríguez-Hertz, Int. Math. Res. Not. IMRN 11, 9469–9481 (2024), Tian, Wu, Nonlinearity 35(1), 658–680 (2022)].