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Sequences of fixed point indices of iterations in dimension 2. (English) Zbl 1061.37016
Let \(f\) be a continuous selfmap of the unit disk \(D^2\) in \({\mathbb R}^2\). If \(x_0\) is an isolated fixed-point of \(f\), \(\text{ind}(f,x_0)\) denotes the local fixed-point index at \(x_0\), that is the fixed-point index of the restriction of \(f\) to an isolating neighborhood of \(x_0\).
Given a sequence of integers \(\{c_n\}_{n\in{\mathbb N}}\) that satisfies the set of congruences known as Dold relations, this paper shows how a function \(f:D^2\to D^2\) can be constructed so that \(c_n=\text{ind}(f^n,0)\) for each \(n\in{\mathbb N}\).

MSC:
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
55M25 Degree, winding number
37E99 Low-dimensional dynamical systems
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