an:00238540
Zbl 0783.58065
Fe??kan, Michal
Invariant curves from symmetry
EN
Math. Bohem. 118, No. 2, 171-174 (1993).
00013962
1993
j
37G15 37B99
invariant curve; discrete dynamical systems
A very nice result is proved in this short paper. Suppose \(m \geq 2\) and \(F:\mathbb{R}^ m \to \mathbb{R}^ m\) is a continuous map. If there are two points in \(\mathbb{R}^ m\) such that one of them is moved closer to the origin by \(F\) while the other is moved farther away and if the map \(F\) is equivariant under the action of a compact subgroup of the orthogonal group that is transitive on the unit sphere, then \(F\) has an invariant curve such that the action of \(F\) on this invariant curve is equivalent to a rotation.
C.Chicone (Columbia)