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The author is partially supported by the National Natural Science Foundation of China (grant no. 11371246).We study holomorphic maps of C2 tangent to the identity at fixed point which have degenerate characteristic directions. With the help of some new invariants, we give suficient conditions for the existence of attracting domains in these degenerate characteristic directions

New invariants and attracting domains for holomorphic maps in $\mathbf{C}^2$ tangent to the identity