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According to \\cite{GL}, after replacing $f$ by a suitable iterate if necessary, we can assume that there exists a minimal set $\\Lambda$ of the action, included in $Fix(f)$.\n  Here, we suppose that $f$ and $h$ are $C^1$ in neighbourhood of $\\Lambda$ and any point $x\\in\\Lambda$ admits an $h$-unstable manifold $W^u(x)$. 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