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<p>In this paper, we make several contributions to the theory of asymptotically sectional-hyperbolic (ASH) flows. First, we prove that every star ASH attractor for a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(C^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation> vector field is, in fact, sectional-hyperbolic (SH). Second, we establish that all ASH attractors exhibit the intermediate entropy property. Additionally, we show that any ASH attractor for three-dimensional vector fields is entropy-expansive and admits periodic orbits. Finally, we provide a lower bound for the growth rate of periodic orbits in an ASH attractor.</p>

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Contributions to the theory of asymptotically sectional hyperbolic flows

  • 期刊论文

  • 发表日期：

    2026年3月24日

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  • Alexander Arbieto,
  • Miguel Pineda,
  • Elias Rego,
  • Kendry Vivas

摘要

In this paper, we make several contributions to the theory of asymptotically sectional-hyperbolic (ASH) flows. First, we prove that every star ASH attractor for a \(C^1\) C 1 vector field is, in fact, sectional-hyperbolic (SH). Second, we establish that all ASH attractors exhibit the intermediate entropy property. Additionally, we show that any ASH attractor for three-dimensional vector fields is entropy-expansive and admits periodic orbits. Finally, we provide a lower bound for the growth rate of periodic orbits in an ASH attractor.