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 -