A non-ergodic phenomenon for some random dynamical system

• Autorzy: Komisarski A.
• Języki publikacji: EN

Abstrakty

EN

In [2] Jajte formulated the following question: Let h₀ (x) and h₁ (x) be homeomorphisms of the interval [0, 1] onto itself. Is it true that for any x € [0, 1] and almost any t ϵ (0, 1) there exists a limit of a sequence [formula] for n → ∞, where t = (0, t₁ t₂…)₂ is a binary representation of t, i.e. t = Σ_{i ≥ 1} t_i 2^-i and t_i ϵ {0, 1}? The answer is negative. We describe the set of condensation points of the sequence in some special cases.

Słowa kluczowe

EN

homeomorphisms; random dynamical system; ergodic theorems; non-ergodic phenomenon

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 1999
• Tom: Vol. 19, Fasc. 2
• Strony: 407--412
• Opis fizyczny: Bibliogr. 2 poz.

Twórcy

autor

Komisarski A.

• Department of Mathematics, Warsaw University, ul. Banacha 2, 02-047 Warszawa, Poland

Bibliografia

• [1] W. Feller, An Introduction to Probability Theory and Its Applications, Wiley, New York 1966.
• [2] R. Jajte, Problem 98*, Wiadom. Mat. 7 (1964), p. 251.