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1
Content available remote

Krengel-Lin decomposition for noncompact groups

100%
Bartoszek W., Rębowski R.
Colloquium Mathematicum
|
1996
|
tom 69
|
nr 1
87-94
2
Content available remote

'The mother of all continued fractions'

100%
Dajani K., Kraaikamp C.
Colloquium Mathematicum
|
2000
|
tom 84/85
|
nr 1
109-123
EN
We give the relationship between regular continued fractions and Lehner fractions, using a procedure known as insertion}. Starting from the regular continued fraction expansion of any real irrational x, when the maximal number of insertions is applied one obtains the Lehner fraction of x. Insertions (and singularizations) show how these (and other) continued fraction expansions are related. We also investigate the relation between Lehner fractions and the Farey expansion (also known as the full continued fraction), and obtain the ergodic system underlying the Farey expansion.
3
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Mixing properties of nearly maximal entropy measures for $ℤ^{d}$ shifts of finite type

100%
E. Arthur Robinson, Jr., Şahin A. A.
Colloquium Mathematicum
|
2000
|
tom 84/85
|
nr 1
43-50
EN
We prove that for a certain class of $ℤ^d$ shifts of finite type with positive topological entropy there is always an invariant measure, with entropy arbitrarily close to the topological entropy, that has strong metric mixing properties. With the additional assumption that there are dense periodic orbits, one can ensure that this measure is Bernoulli.
4
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Ergodic theory approach to chaos: Remarks and computational aspects

88%
Mitkowski P., Mitkowski W.
International Journal of Applied Mathematics and Computer Science
|
2012
|
tom 22
|
nr 2
259-267
EN
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 of a nonsimple structure, supporting an invariant mixing measure. This observation verifies Lasota's conjecture concerning nontrivial ergodic properties of the model.
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