Limit sets, attractors and chaos (Q1707518)

The authors strengthen the notion of \(\omega\)-chaos, which uses pairs of points, to \(\hat{\omega}\)-chaos, which is defined with \(n\)-tuples, where \(n\) is allowed to range over natural numbers. The following examples are constructed: 1. An \(\hat{\omega}\)-chaotic Cantor subset of a one-sided binary shift. 2. For every \(n\geq 2\), a continuous \(\hat{\omega}\)-chaotic self-map of \([0,1]^n\) with a Mycielski \(\hat{\omega}\)-scrambled set of measure 1. 3. A transitive \(\hat{\omega}\)-chaotic triangular self-map of \([0,1]^2\) with a dense Mycielski \(\hat{\omega}\)-scrambled set. 4. An almost equicontinuous \(\hat{\omega}\)-chaotic homeomorphism of a compact space.