Automorphismes analytiques admettant des sous-variétés de points fixés attractives dans la direction transversale
Let T be an automorphism of the complex manifold X, and let T have the complex submanifold \(Y\subset X\) as a set of fixed points. Then T induces an automorphism L of the normal bundle N of Y. If, in addition, Y is attractive relative to T then the set \(\Omega\) of points \(x\in X\), such that the sequence T(x), \(T^ 2(x),..\). converges toward a point of Y forms an open set containing Y. In this situation, the author proves: If the eigenvalues of T are unrelated at each point of Y, then there exists a biholomorphic map S:\(N\to \Omega\) such that \(T\circ S=S\circ L;\) moreover, S satisfies a certain normalizing condition, and is uniquely determined by it.
submanifold fixed by analytic automorphism
scientific article; zbMATH DE number 3867720