Ergodic theory of differentiable dynamical systems

David Ruelle

Displaying similar documents to “Ergodic theory of differentiable dynamical systems”

Ratio limit theorems and applications to ergodic theory

Ryotaro Sato (1980)

Studia Mathematica

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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 $n^{- 1} \sum_{i = 0}^{n - 1} f \circ τ^{i} (x)$ 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 $(r, s) : r = s = 1, o r 1 < r < \infty a n d 1 \leq s \leq \infty, o r r = s = \infty$ . Results due to C. Ryll-Nardzewski, S. Gładysz, and I. Assani and J. Woś are generalized...

On the ergodic theorems (I) (Generalized ergodic theorems)

C. Ryll-Nardzewski (1951)

Studia Mathematica

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Existence of non-uniform cocycles on uniquely ergodic systems

Daniel Lenz (2004)

Annales de l'I.H.P. Probabilités et statistiques

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On the ergodic theorems (II) (Ergodic theory of continued fractions)

C. Ryll-Nardzewski (1951)

Studia Mathematica

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Mixtures of invariant non-ergodic probabilities

Rao, M.B. (1978)

Portugaliae mathematica

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On functions with scattered spectra on lea groups

Paweł Głowacki (1981)

Studia Mathematica

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On non-ergodic versions of limit theorems

Dalibor Volný (1989)

Aplikace matematiky

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The author investigates non ergodic versions of several well known limit theorems for strictly stationary processes. In some cases, the assumptions which are given with respect to general invariant measure, guarantee the validity of the theorem with respect to ergodic components of the measure. In other cases, the limit theorem can fail for all ergodic components, while for the original invariant measure it holds.