Dense chaos for continuous interval maps
نویسندگان
چکیده
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 shall consider slightly more general problems. Namely, we shall investigate the existence of continuous: piecewise monotone, piecewise strictly monotone, and piecewise linear n-th roots of interval maps which have a continuous n-th root. Here by an n-th root of f we mean a map g such that f = g (g is the n-th iterate of g). A continuous map f : I → J , where I, J are closed intervals, is pie...
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In this note, we present a simple one-parameter family of interval maps which has a direct bifurcation from order to chaos and then another direct bifurcation from chaos back to order. (See also [4, 5].) In fact, for this family of interval maps, the creation of the first non-fixed periodic point is more complicated than we expect. It is the limit point of a series of bifurcations of period 2n ...
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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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For continuous maps of an interval into itself we consider cycles (periodic orbits) that are non-reducible in the sense that there is no non-trivial partition into blocks of consecutive points permuted by the map. Among them we identify the miror ones. They are those whose existence does not imply existence of other non-reducible cycles of the same period. Moreover, we find minor patterns of a ...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2005
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/18/4/015