ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

On Dynamics of Total Expanding Mappings on R


Sergey Andreevich Brygin

Saint-Petersburg State University,
Universitetskiy Prospect,28
198504, Saint-Petersburg, Russia
Phone +79117008394,

Alexander Alekseevich Florinskiy

Saint-Petersburg State University,
Associated Professor,
PhD in Physics and Mathematics
Universitetskiy Prospect,28
198504, Saint-Petersburg, Russia


In this paper we show that there exists a smooth transformation of real line, such that the sequence of images of any nonempty open set under iterations of this transformation has real line as its lower limit. It is also proved that for such a transformation there always exists a compact set having a dense orbit in the space of all the compact subsets of real line with Hausdorff metric. Some properties of such compact sets are considered.


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