Journal of the
Korean Mathematical Society
JKMS
ISSN(Print) 0304-9914
ISSN(Online) 2234-3008
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J. Korean Math. Soc. 2024; 61(3): 495-513
Online first article April 9, 2024 Printed May 1, 2024
https://doi.org/10.4134/JKMS.j230333
Copyright © The Korean Mathematical Society.
Singular hyperbolicity of $C^1$ generic three dimensional vector fields
Manseob Lee
Mokwon University
In the paper, we show that for a generic $C^1$ vector field $X$ on a closed three dimensional manifold $M$, any isolated transitive set of $X$ is singular hyperbolic. It is a partial answer of the conjecture in \cite{MP}.
Keywords: Transitive set, generic, local star, Lyapunove stable, singular hyperbolic
MSC numbers: Primary 37C20, 37C27, 37D50
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