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Continuum-wise expansiveness for $C^1$ generic vector fields

이만섭
대한수학회 (The Korean Mathematical Society)|2023.09|대한수학회지 (Journal of the KMS)|제60권 제5호|pp. 987-998|DOI 10.4134/JKMS.j220359

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참고문헌

키워드

homoclinic classgenericAxiom AhyperbolicExpansivecontinuum-wise expansive
주제분류수학

초록

It is shown that every continuum-wise expansive $C^1$ generic vector field $X$ on a compact connected smooth manifold $M$ satisfies Axiom A and has no cycles, and every continuum-wise expansive homoclinic class of a $C^1$ generic vector field $X$ on a compact connected smooth manifold $M$ is hyperbolic. Moreover, every continuum-wise expansive $C^1$ generic divergence-free vector field $X$ on a compact connected smooth manifold $M$ is Anosov.

Abstract

It is shown that every continuum-wise expansive $C^1$ generic vector field $X$ on a compact connected smooth manifold $M$ satisfies Axiom A and has no cycles, and every continuum-wise expansive homoclinic class of a $C^1$ generic vector field $X$ on a compact connected smooth manifold $M$ is hyperbolic. Moreover, every continuum-wise expansive $C^1$ generic divergence-free vector field $X$ on a compact connected smooth manifold $M$ is Anosov.

참고문헌 (39)

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