Local Distributional Chaos

Distributional chaos was introduced in Schweizer and Smítal (Trans Am Math Soc 344:737–754, 1994) for continuous maps of the interval, as chaotic behavior based on development distances between orbits points system. In Balibrea et al. (Chaos Solitons Fractals 23(5):1581–1583, 2005), this phenomenon generalized to compact metric space distinguished into three different forms, DC1, DC2 DC3. Loranty Pawlak 29:013104, 2019), local idea such is studied, which leads definition distributionally (DC-points). It also proved (2019), that interval maps, positive topological entropy implies existence DC1-point. paper result strengthened; it an uncountable set DC1-points, moreover can be chosen perfect. greater dimensions than one, we deal with triangular systems $$I^{2}$$ . case relationship types distributional not clearly understood several results are possible. use example map F given by Kolyada (Ergod Theory Dyn Syst 12:749–768, 1992) prove corresponding two dimensional system $$(I^ {2}, F)$$ has but without containing DC2-points, proving there no concentration DC2-chaos.