Fixed point indices of iterated smooth maps in arbitrary dimension

Let f be a smooth self-map of Rm, when m is an arbitrary natural number. We give a complete description of possible sequences of indices of iterations of f at an isolated fixed point, answering in affirmative the Chow, Mallet-Paret and Yorke conjecture posed in [S.N. Chow, J. Mallet-Parret, J.A. Yorke, A periodic point index which is a bifurcation invariant, in: Geometric Dynamics, Rio de Janeiro, 1981, in: Lecture Notes in Math., vol. 1007, Springer, Berlin, 1983, pp. 109–131].