Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
On the dynamics of total expansions of the real line. / Brygin, S. A.; Florinskii, A. A.
в: Differential Equations, Том 50, № 13, 01.01.2014, стр. 1691-1694.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - On the dynamics of total expansions of the real line
AU - Brygin, S. A.
AU - Florinskii, A. A.
PY - 2014/1/1
Y1 - 2014/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84961378862&partnerID=8YFLogxK
U2 - 10.1134/S0012266114130011
DO - 10.1134/S0012266114130011
M3 - Article
AN - SCOPUS:84961378862
VL - 50
SP - 1691
EP - 1694
JO - Differential Equations
JF - Differential Equations
SN - 0012-2661
IS - 13
ER -
ID: 50053000