Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Distributionally chaotic maps are $ C^0$-dense


Author: Noriaki Kawaguchi
Journal: Proc. Amer. Math. Soc. 147 (2019), 5339-5348
MSC (2010): Primary 74H65, 37C50, 37B40
DOI: https://doi.org/10.1090/proc/14696
Published electronically: July 9, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the set of maps which exhibit distributional chaos of type 1 (DC1) is $ C^0$-dense in the space of continuous self-maps of given any compact topological manifold (possibly with boundary).


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 74H65, 37C50, 37B40

Retrieve articles in all journals with MSC (2010): 74H65, 37C50, 37B40


Additional Information

Noriaki Kawaguchi
Affiliation: Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba Meguro, Tokyo 153-8914, Japan
Email: knoriaki@ms.u-tokyo.ac.jp

DOI: https://doi.org/10.1090/proc/14696
Keywords: Distributional chaos, topological manifold, limit shadowing, entropy
Received by editor(s): November 17, 2018
Received by editor(s) in revised form: February 26, 2019
Published electronically: July 9, 2019
Communicated by: Nimish Shah
Article copyright: © Copyright 2019 American Mathematical Society