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Attractors with the symmetry of the \(n\)-cube. (English) Zbl 0885.58043
The author studies and describes in detail the equivariant polynomial maps of \(\mathbb{R}^n\) (Theorem 2.2), i.e., those maps \(P: \mathbb{R}^n \to\mathbb{R}^n\) which are polynomials and satisfy the conditions \(P(\rho(x))= \rho(P(x))\) for all \(x\in \mathbb{R}^n\) and all orientation-preserving symmetries \(\rho\) of the \(n\)-cube.
Furthermore, some aspects of the dynamical behaviour of some examples in dimensions 2 up to 4 of linear combinations of such equivariant polynomials are studied by experiments and their attractors are visualized. (In the 4-dimensional case a central projection of the 4-cube is used for the illustration of the attractor).

MSC:
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
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