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A mapping f: R → R is called a total expansion if (Formula presented.) and (Formula presented.) for all a < b ∈ R; here fn stands for the nth iteration of f. We prove that there exists a smooth total expansion f: R → R such that one of its orbits is a given countable everywhere dense set. We also prove that, for each total expansion f: R → R, there exists a compact set K ⊂ R, referred to as an f-universal compact set, such that the sequence fn(K) is dense in the space Comp(R) of all nonempty compact subsets of R with the Hausdorff metric.
Original language | English |
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Pages (from-to) | 1691-1694 |
Number of pages | 4 |
Journal | Differential Equations |
Volume | 50 |
Issue number | 13 |
DOIs | |
State | Published - 1 Jan 2014 |
ID: 50053000