Links of homeomorphisms of a disk and topological entropy
For f an orientation preserving homeomorphism of a disc \({\mathbb{D}}^ 2\) with a finite f-invariant set \(\Sigma =\{p_ 1,...,p_ n\}\) of periodic points in int \({\mathbb{D}}^ 2\) a condition which implies chaos (positive entropy) is found. This condition concerns the link given by the simple closed curves of the suspension (\(\Sigma\),f) in the solid torus - the suspension \(({\mathbb{D}}^ 2,f)\) (more exactly the link in \(S^ 3\), the equator of the complementary solid torus added). In other words the condition concerns an isotopy class of \(Diff({\mathbb{D}}^ 2,\Sigma)\) to which a diffeomorphism isotopic to f belongs. The theory of 3-manifolds and pseudo-Anosov homeomorphisms is used.
orientation preserving homeomorphism of a disc
scientific article; zbMATH DE number 3938047