On measures of chaos for distributionally chaotic maps. (English) Zbl 1116.37014

Janková, Katarína

Real Anal. Exch. 32(2006-2007), No. 1, 213-219 (2007).

Summary: Let \(f\) be a distributionally chaotic map of the interval such that the endpoints of the minimal periodic portions of any basic set are periodic. Then the principal measure of chaos, \(\mu_p(f)\), is not greater than twice the spectral measure of chaos \(\mu_s(f)\). This proves an assertion of Schweizer et al. in a special case.

MSC:

37B99	Topological dynamics
37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior
26A18	Iteration of real functions in one variable

Keywords:

distributional chaos; principal measure of chaos; spectral measure of chaos; \(\omega\)-limit set