Displaying similar documents to “Absolutely continuous, invariant measures for dissipative, ergodic transformations”

On a pointwise ergodic theorem for multiparameter semigroups.

Ryotaro Sato (1994)

Publicacions Matemàtiques

Similarity:

Let Ti (i = 1, 2, ..., d) be commuting null preserving transformations on a finite measure space (X, F, μ) and let 1 ≤ p < ∞. In this paper we prove that for every f ∈ Lp(μ) the averages Anf(x) = (n + 1)-d Σ0≤ni≤n f(T1 n1 T2 n2...

Genericity of nonsingular transformations with infinite ergodic index

J. Choksi, M. Nadkarni (2000)

Colloquium Mathematicae

Similarity:

It is shown that in the group of invertible measurable nonsingular transformations on a Lebesgue probability space, endowed with the coarse topology, the transformations with infinite ergodic index are generic; they actually form a dense G δ set. (A transformation has infinite ergodic index if all its finite Cartesian powers are ergodic.) This answers a question asked by C. Silva. A similar result was proved by U. Sachdeva in 1971, for the group of transformations preserving an infinite...

Ergodic theory approach to chaos: Remarks and computational aspects

Paweł J. Mitkowski, Wojciech Mitkowski (2012)

International Journal of Applied Mathematics and Computer Science

Similarity:

We discuss basic notions of the ergodic theory approach to chaos. Based on simple examples we show some characteristic features of ergodic and mixing behaviour. Then we investigate an infinite dimensional model (delay differential equation) of erythropoiesis (red blood cell production process) formulated by Lasota. We show its computational analysis on the previously presented theory and examples. Our calculations suggest that the infinite dimensional model considered possesses an attractor...

A joint limit theorem for compactly regenerative ergodic transformations

David Kocheim, Roland Zweimüller (2011)

Studia Mathematica

Similarity:

We study conservative ergodic infinite measure preserving transformations satisfying a compact regeneration property introduced by the second-named author in J. Anal. Math. 103 (2007). Assuming regular variation of the wandering rate, we clarify the asymptotic distributional behaviour of the random vector (Zₙ,Sₙ), where Zₙ and Sₙ are respectively the time of the last visit before time n to, and the occupation time of, a suitable set Y of finite measure.

Exactness of skew products with expanding fibre maps

Thomas Bogenschütz, Zbigniew Kowalski (1996)

Studia Mathematica

Similarity:

We give an elementary proof for the uniqueness of absolutely continuous invariant measures for expanding random dynamical systems and study their mixing properties.

Pointwise ergodic theorems in Lorentz spaces L(p,q) for null preserving transformations

Ryotaro Sato (1995)

Studia Mathematica

Similarity:

Let (X,ℱ,µ) be a finite measure space and τ a null preserving transformation on (X,ℱ,µ). Functions in Lorentz spaces L(p,q) associated with the measure μ are considered for pointwise ergodic theorems. Necessary and sufficient conditions are given in order that for any f in L(p,q) the ergodic average n - 1 ∑ i = 0 n - 1 f ∘ τ i ( x ) converges almost everywhere to a function f* in L ( p 1 , q 1 ] , where (pq) and ( p 1 , q 1 ] are assumed to be in the set ( r , s ) : r = s = 1 , o r 1 < r < ∞ a n d 1 ≤ s ≤ ∞ , o r r = s = ∞ . Results due to C. Ryll-Nardzewski, S. Gładysz, and I. Assani and J. Woś are generalized...