Artykuły w formacie PDF dostępne są dla subskrybentów, którzy zapłacili za dostęp online, po pospisaniu licencji Licencja użytkownika instytucjonalnego. Czasopisma do 2008 są ogólnodostępne (bezpłatnie).

On the $\omega$-limit sets of tent maps

Tom 217 / 2012

Andrew D. Barwell, Gareth Davies, Chris Good Fundamenta Mathematicae 217(2012), 35-54 MSC: 37B10, 37C50, 37E05, 54C05, 54H20. DOI: 10.4064/fm217-1-4 Opublikowany online: 1 January 1970

Streszczenie

For a continuous map $f$ on a compact metric space $(X,d)$, a set $D\subset X$ is internally chain transitive if for every $x,y\in D$ and every $\delta>0$ there is a sequence of points $\langle x=x_0,x_1,\ldots,x_n=y\rangle$ such that $d(f(x_i),x_{i+1})< \delta$ for $0\leq i< n$. In this paper, we prove that for tent maps with periodic critical point, every closed, internally chain transitive set is necessarily an $\omega$-limit set. Furthermore, we show that there are at least countably many tent maps with non-recurrent critical point for which there is a closed, internally chain transitive set which is not an $\omega$-limit set. Together, these results lead us to conjecture that for tent maps with shadowing, the $\omega$-limit sets are precisely those sets having internal chain transitivity.

Autorzy

  • Andrew D. BarwellSchool of Mathematics
    University of Bristol
    Howard House
    Queens Avenue
    Bristol, BS8 1SN, UK
    and
    School of Mathematics
    University of Birmingham
    Birmingham, B15 2TT, UK
    e-mail
  • Gareth DaviesMathematical Institute
    University of Oxford
    24-29 St. Giles'
    Oxford, OX1 3LB, UK
    e-mail
  • Chris GoodSchool of Mathematics
    University of Birmingham
    Birmingham, B15 2TT, UK
    e-mail

Przeszukaj wydawnictwa

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek