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<p>In this article, we investigate expansivity, Li–Yorke chaos and shadowing properties for composition operators <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="574_2024_435_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="93" /> </InlineMediaObject> <EquationSource Format="TEX">\(C_{\phi }f = f \circ \phi \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>C</mi> <mi>ϕ</mi> </msub> <mi>f</mi> <mo>=</mo> <mi>f</mi> <mo>∘</mo> <mi>ϕ</mi> </mrow> </math></EquationSource> </InlineEquation> induced by affine self-maps <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="574_2024_435_Article_IEq4.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(\phi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϕ</mi> </math></EquationSource> </InlineEquation> of the right half-plane <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="574_2024_435_Article_IEq5.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {C}}_{+}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">C</mi> <mo>+</mo> </msub> </math></EquationSource> </InlineEquation> on the Hardy–Hilbert space <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="574_2024_435_Article_IEq6.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(H^{2}(\mathbb {C_{+}})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>H</mi> <mn>2</mn> </msup> <mrow> <mo stretchy="false">(</mo> <msub> <mi mathvariant="double-struck">C</mi> <mo>+</mo> </msub> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Dynamical Properties for Composition Operators on \(H^{2}({\mathbb {C}}_{+})\)

  • 期刊论文

  • 发表日期：

    2025年1月8日

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  • Carlos F. Álvarez,
  • Javier Henríquez-Amador

摘要

In this article, we investigate expansivity, Li–Yorke chaos and shadowing properties for composition operators \(C_{\phi }f = f \circ \phi \) C ϕ f = f ∘ ϕ induced by affine self-maps \(\phi \) ϕ of the right half-plane \({\mathbb {C}}_{+}\) C + on the Hardy–Hilbert space \(H^{2}(\mathbb {C_{+}})\) H 2 ( C + ) .