In this paper we investigate numerous constructions of minimal systems from the point of view of -chaos (but most of our results concern the particular cases of distributional chaos of type and ). We consider standard classes of systems, such as Toeplitz flows, Grillenberger -systems or Blanchard-Kwiatkowski extensions of the Chacón flow, proving that all of them are DC2. An example of DC1 minimal system with positive topological entropy is also introduced. The above mentioned results answer a few open problems known from the literature.
Keywords: chaotic pair, scrambled set, Mycielski set, distributional chaos, Li-Yorke chaos, filter
Mot clés : paire chaotique, ensemble ***, ensemble de Mycielski, chaos distributionnel, chaos de Li-Yorke, filtre
@article{BSMF_2012__140_3_401_0, author = {Oprocha, Piotr}, title = {Minimal systems and distributionally scrambled sets}, journal = {Bulletin de la Soci\'et\'e Math\'ematique de France}, pages = {401--439}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {140}, number = {3}, year = {2012}, doi = {10.24033/bsmf.2631}, zbl = {1278.37013}, language = {en}, url = {http://www.numdam.org/articles/10.24033/bsmf.2631/} }
TY - JOUR AU - Oprocha, Piotr TI - Minimal systems and distributionally scrambled sets JO - Bulletin de la Société Mathématique de France PY - 2012 SP - 401 EP - 439 VL - 140 IS - 3 PB - Société mathématique de France UR - http://www.numdam.org/articles/10.24033/bsmf.2631/ DO - 10.24033/bsmf.2631 LA - en ID - BSMF_2012__140_3_401_0 ER -
%0 Journal Article %A Oprocha, Piotr %T Minimal systems and distributionally scrambled sets %J Bulletin de la Société Mathématique de France %D 2012 %P 401-439 %V 140 %N 3 %I Société mathématique de France %U http://www.numdam.org/articles/10.24033/bsmf.2631/ %R 10.24033/bsmf.2631 %G en %F BSMF_2012__140_3_401_0
Oprocha, Piotr. Minimal systems and distributionally scrambled sets. Bulletin de la Société Mathématique de France, Volume 140 (2012) no. 3, pp. 401-439. doi : 10.24033/bsmf.2631. http://www.numdam.org/articles/10.24033/bsmf.2631/
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