Let f: X→ X be a topologically transitive continuous map of a compact metric space X. We investigate whether f can have the following stronger properties: (i) for each m ∈ ℕ, is transitive, (ii) for each m ∈ ℕ, there exists x ∈ X such that the diagonal m-tuple (x,x,...,x) has a dense orbit in under the action of . We show that (i), (ii) and weak mixing are equivalent for minimal homeomorphisms, that all mixing interval maps satisfy (ii), and that there are mixing subshifts not satisfying (ii).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm120-1-9, author = {T. K. Subrahmonian Moothathu}, title = {Diagonal points having dense orbit}, journal = {Colloquium Mathematicae}, volume = {120}, year = {2010}, pages = {127-138}, zbl = {1200.54020}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm120-1-9} }
T. K. Subrahmonian Moothathu. Diagonal points having dense orbit. Colloquium Mathematicae, Tome 120 (2010) pp. 127-138. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm120-1-9/