| Summary: | In this paper, we prove that for a generically <inline-formula><math display="inline"><semantics><msup><mi>C</mi><mn>1</mn></msup></semantics></math></inline-formula> vector field <i>X</i> of a compact smooth manifold <i>M</i>, if a homoclinic class <inline-formula><math display="inline"><semantics><mrow><mi>H</mi><mo>(</mo><mi>γ</mi><mo>,</mo><mi>X</mi><mo>)</mo></mrow></semantics></math></inline-formula> which contains a hyperbolic closed orbit <inline-formula><math display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> is measure expansive for <i>X</i> then <inline-formula><math display="inline"><semantics><mrow><mi>H</mi><mo>(</mo><mi>γ</mi><mo>,</mo><mi>X</mi><mo>)</mo></mrow></semantics></math></inline-formula> is hyperbolic.
|
|---|