A note on dynamics in functional spaces

LIANGXUE PENG; Chong YANG

Article Details

A note on dynamics in functional spaces

Authors:

LIANGXUE PENG | Chong YANG

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2017 Vol.41 Issue 1, pp.186-192

Document Type:

Article

Publication Date:

1/2017

Document Language:

Turkish

Document ID (Org No.):

2000746096

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Abstract:

 

In this note, we study topologically transitive and hypercyclic composition operators on  Cp(X)Cp(X)C_p(X) or Ck(X)Ck(X)C_k(X).  We prove that if GGG is a semigroup of continuous self maps of a countable metric space XXX  with the following properties:  (1) every element of GGG is one-to-one on XXX,  (2) the action of GGG is strongly run-away on XXX,  then the action of ^GG^\hat{G} on Cp(X)Cp(X)C_p(X) is topologically transitive and hypercyclic.  If GGG is the set of all one-to-one and continuous self maps of R∖ZR∖Z\mathbb{R}\setminus \mathbb{Z},  then the action of ^GG^\hat{G} on Ck(R∖Z)Ck(R∖Z)C_k(\mathbb{R}\setminus \mathbb{Z}) is hypercyclic.  We also show that the action of ^GG^\hat{G}  on Cp(ω1)Cp(ω1)C_p(\omega_1) is not hypercyclic.

Article Details

A note on dynamics in functional spaces

Authors: LIANGXUE PENG | Chong YANG

Publisher: TUBITAK

Journal: Turkish Journal of Mathematics 2017 Vol.41 Issue 1, pp.186-192

Document Type: Article

Publication Date: 1/2017

Document Language: Turkish

Document ID (Org No.): 2000746096

Frequency: Bimonthly

eISSN: 1303-6149

pISSN: 1300-0098

Issues

Authors:

LIANGXUE PENG | Chong YANG

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2017 Vol.41 Issue 1, pp.186-192

Document Type:

Article

Publication Date:

1/2017

Document Language:

Turkish

Document ID (Org No.):

2000746096

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098