# THE LOCAL STAR CONDITION FOR GENERIC TRANSITIVE DIFFEOMORPHISMS

Lee, Manseob

• Published : 2016.04.30
• 12 1

#### Abstract

Let $f:M{\rightarrow}M$ be a diffeomorphism on a closed $C^{\infty}\;d({\geq}2)$ dimensional manifold M. For $C^1$-generic f, if a diffeomorphism f satisfies the local star condition on a transitive set, then it is hyperbolic.

#### Keywords

transitive set;star diffeomorphisms;local star diffeomorphisms;hyperbolic

#### References

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#### Acknowledgement

Supported by : National Research Foundation of Korea (NRF)