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Sequence entropy pairs and complexity pairs for a measure

Wen Huang, Alejandro Maass, Xiangdong Ye (2004)

Annales de l’institut Fourier

In this paper we explore topological factors in between the Kronecker factor and the maximal equicontinuous factor of a system. For this purpose we introduce the concept of sequence entropy n -tuple for a measure and we show that the set of sequence entropy tuples for a measure is contained in the set of topological sequence entropy tuples [H- Y]. The reciprocal is not true. In addition, following topological ideas in [BHM], we introduce a weak notion and a strong notion of complexity pair for a...

Spectrum of multidimensional dynamical systems with positive entropy

B. Kamiński, P. Liardet (1994)

Studia Mathematica

Applying methods of harmonic analysis we give a simple proof of the multidimensional version of the Rokhlin-Sinaǐ theorem which states that a Kolmogorov ℤ d -action on a Lebesgue space has a countable Lebesgue spectrum. At the same time we extend this theorem to ℤ ∞ -actions. Next, using its relative version, we extend to ℤ ∞ -actions some other general results connecting spectrum and entropy.

Spontaneous clustering in theoretical and some empirical stationary processes*

T. Downarowicz, Y. Lacroix, D. Léandri (2010)

ESAIM: Probability and Statistics

In a stationary ergodic process, clustering is defined as the tendency of events to appear in series of increased frequency separated by longer breaks. Such behavior, contradicting the theoretical “unbiased behavior” with exponential distribution of the gaps between appearances, is commonly observed in experimental processes and often difficult to explain. In the last section we relate one such empirical example of clustering, in the area of marine technology. In the theoretical part of the paper...

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