منابع مشابه
On the Invariance of Li-Yorke Chaos of Interval Maps
In their celebrated ”Period three implies chaos” paper, Li and Yorke proved that if a continuous interval map f has a period 3 point then there is an uncountable scrambled set S on which f has very complicated dynamics. One question arises naturally: Can this set S be chosen invariant under f? The answer is positive for turbulent maps and negative otherwise. In this note, we shall use symbolic ...
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We study exactness and maximal automorphic factors of C3 unimodal maps of the interval. We show that for a large class of infinitely renormalizable maps, the maximal automorphic factor is an odometer with an ergodic non-singular measure. We give conditions under which maps with absorbing Cantor sets have an irrational rotation on a circle as a maximal automorphic factor, as well as giving exact...
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Y.G. Petalas∗1, E.I. Papageorgiou2, K.E. Parsopoulos1, P.P. Groumpos2 and M.N. Vrahatis1 1 Computational Intelligence Laboratory (CI Lab), Department of Mathematics, University of Patras Artificial Intelligence Research Center (UPAIRC), University of Patras, GR-26110 Patras, Hellas 2 Department of Electrical Engineering, Lab. of Automation and Robotics, University of Patras, GR–26500 Patras, He...
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Dimension groups for interval maps
With each piecewise monotonic map τ of the unit interval, a dimension triple is associated. The dimension triple, viewed as a Z[t, t−1] module, is finitely generated, and generators are identified. Dimension groups are computed for Markov maps, unimodal maps, multimodal maps, and interval exchange maps. It is shown that the dimension group defined here is isomorphic to K0(A), where A is a C*-al...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1980
ISSN: 0040-8735
DOI: 10.2748/tmj/1178229634