An ergodic theorem without invariant measure
R. Sato (1990)
Colloquium Mathematicae
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Displaying similar documents to “Ergodic properties and KMS conditions on -symbolic dynamical systems.”
An ergodic theorem without invariant measure
Ergodic averages and integrals of cocycles.
Keynes, H.B., Markley, N.G., Sears, M. (1995)
Acta Mathematica Universitatis Comenianae. New Series
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Ergodic elements of ergodic actions
Charles Pugh, Michael Shub (1971)
Compositio Mathematica
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Ergodic States in a Non Commutative Ergodic Theory
S. Doplicher, D. Kastler (1968)
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On subrelations of ergodic measured type III equivalence relations
Alexandre Danilenko (2000)
Colloquium Mathematicae
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We discuss the classification up to orbit equivalence of inclusions 𝑆 ⊂ ℛ of measured ergodic discrete hyperfinite equivalence relations. In the case of type III relations, the orbit equivalence classes of such inclusions of finite index are completely classified in terms of triplets consisting of a transitive permutation group G on a finite set (whose cardinality is the index of 𝑆 ⊂ ℛ), an ergodic nonsingular ℝ-flow V and a homomorphism of G to the centralizer of V.
Distal actions and ergodic actions on compact groups.
Raja, C.Robinson Edward (2009)
The New York Journal of Mathematics [electronic only]
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Construction of non-constant and ergodic cocycles
Mahesh Nerurkar (2000)
Colloquium Mathematicae
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We construct continuous G-valued cocycles that are not cohomologous to any compact constant via a measurable transfer function, provided the underlying dynamical system is rigid and the range group G satisfies a certain general condition. For more general ergodic aperiodic systems, we also show that the set of continuous ergodic cocycles is residual in the class of all continuous cocycles provided the range group G is a compact connected Lie group. The first construction is based on...
Pointwise ergodic theorems in Lorentz spaces L(p,q) for null preserving transformations
Ryotaro Sato (1995)
Studia Mathematica
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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 converges almost everywhere to a function f* in , where (pq) and are assumed to be in the set . Results due to C. Ryll-Nardzewski, S. Gładysz, and I. Assani and J. Woś are generalized...
On functions with scattered spectra on lea groups
Paweł Głowacki (1981)
Studia Mathematica
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Ergodic theory approach to chaos: Remarks and computational aspects
Paweł J. Mitkowski, Wojciech Mitkowski (2012)
International Journal of Applied Mathematics and Computer Science
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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...
On the Pointwise Ergodic Theorem in
F. Martín-Reyes, A. de la Torre (1994)
Studia Mathematica
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Ergodic properties of skew products withfibre maps of Lasota-Yorke type
Zbigniew Kowalski (1994)
Applicationes Mathematicae
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We consider the skew product transformation T(x,y)= (f(x), ) where f is an endomorphism of a Lebesgue space (X,A,p), e : X → S and is a family of Lasota-Yorke type maps of the unit interval into itself. We obtain conditions under which the ergodic properties of f imply the same properties for T. Consequently, we get the asymptotical stability of random perturbations of a single Lasota-Yorke type map. We apply this to some probabilistic model of the motion of cogged bits in the rotary...