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Fixed point indices of iterations of \(C^1\) maps in \(\mathbb R^3\). (English) Zbl 1185.37043
Summary: In the case of a \(C^1\) self-map of \(\mathbb R^3\) we prove the Chow, Mallet-Paret and Yorke conjecture [Geometric dynamics, Proc. int. Symp., Rio de Janeiro/Brasil 1981, Lect. Notes Math. 1007, 109–131 (1983; Zbl 0549.34045)] on the form of sequences of local fixed point indices of iterations and give a complete description of possible sequences of indices.

MSC:
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
37C05 Dynamical systems involving smooth mappings and diffeomorphisms
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