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Abstract <p> On a Riemannian manifold of dimension <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(m\ge 3\)</EquationSource> </InlineEquation>, we considera nonempty compact set <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(A\)</EquationSource> </InlineEquation> that is invariant forsome <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(C^1\)</EquationSource> </InlineEquation>-smooth flow. Sufficient conditions under which<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(A\)</EquationSource> </InlineEquation> is a hyperbolic set of the flow are proposed.</p>

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Sufficient Hyperbolicity Conditions for Flows

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • S. D. Glyzin,
  • A. Yu. Kolesov

摘要

Abstract

On a Riemannian manifold of dimension \(m\ge 3\) , we considera nonempty compact set \(A\) that is invariant forsome \(C^1\) -smooth flow. Sufficient conditions under which \(A\) is a hyperbolic set of the flow are proposed.