Diagonal points having dense orbit

• Autorzy: T. K. Subrahmonian Moothathu
• Języki publikacji: EN

Abstrakty

EN

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, $f × f² × ⋯ × f^{m}: X^{m} → X^{m}$ 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 $X^{m}$ under the action of $f × f² × ⋯ × f^{m}$. 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).

Kategorie tematyczne

• 54H20: Topological dynamics
• 37B20: Notions of recurrence
• 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 120
• Numer: 1
• Strony: 127-138

Daty

wydano

2010

Twórcy

autor

T. K. Subrahmonian Moothathu

• Department of Mathematics and Statistics, University of Hyderabad, Hyderabad 500 046, India

Identyfikatory

DOI

10.4064/cm120-1-9