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We prove some results concerning the entropy of Darboux (and almost continuous) functions. We first generalize some theorems valid for continuous functions, and then we study properties which are specific to Darboux functions. Finally, we give theorems on approximating almost continuous functions by functions with infinite entropy.
Ryszard J. Pawlak. "On the entropy of Darboux functions." Colloquium Mathematicae 116.2 (2009): 227-241. <http://eudml.org/doc/283766>.
@article{RyszardJ2009, abstract = {We prove some results concerning the entropy of Darboux (and almost continuous) functions. We first generalize some theorems valid for continuous functions, and then we study properties which are specific to Darboux functions. Finally, we give theorems on approximating almost continuous functions by functions with infinite entropy.}, author = {Ryszard J. Pawlak}, journal = {Colloquium Mathematicae}, keywords = {topological entropy; Darboux function; almost fixed point; almost continuity; periodic point; -horseshoe; turbulent function; -approximation}, language = {eng}, number = {2}, pages = {227-241}, title = {On the entropy of Darboux functions}, url = {http://eudml.org/doc/283766}, volume = {116}, year = {2009}, }
TY - JOUR AU - Ryszard J. Pawlak TI - On the entropy of Darboux functions JO - Colloquium Mathematicae PY - 2009 VL - 116 IS - 2 SP - 227 EP - 241 AB - We prove some results concerning the entropy of Darboux (and almost continuous) functions. We first generalize some theorems valid for continuous functions, and then we study properties which are specific to Darboux functions. Finally, we give theorems on approximating almost continuous functions by functions with infinite entropy. LA - eng KW - topological entropy; Darboux function; almost fixed point; almost continuity; periodic point; -horseshoe; turbulent function; -approximation UR - http://eudml.org/doc/283766 ER -