- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 673578, 7 pages
DC3 Pairs and the Set of Discontinuities in Distribution Functions
1Department of Mathematics, Dalian Nationalities University, Dalian 116600, China
2AGH University of Science and Technology, Faculty of Applied Mathematics, Aleja A. Mickiewicza 30, 30-059 Kraków, Poland
3Institute of Mathematics, Polish Academy of Sciences, Ulica Śniadeckich 8, 00-956 Warszawa, Poland
4School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
Received 18 April 2013; Accepted 21 June 2013
Academic Editor: Guang Zhang
Copyright © 2013 Lidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- B. Schweizer and J. Smítal, “Measures of chaos and a spectral decomposition of dynamical systems on the interval,” Transactions of the American Mathematical Society, vol. 344, no. 2, pp. 737–754, 1994.
- T. Y. Li and J. A. Yorke, “Period three implies chaos,” The American Mathematical Monthly, vol. 82, no. 10, pp. 985–992, 1975.
- R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley Studies in Nonlinearity, Addison-Wesley Publishing Company, Advanced Book Program, Redwood City, CA, USA, 2nd edition, 1989.
- H. Wang, G. Liao, and Q. Fan, “Substitution systems and the three versions of distributional chaos,” Topology and Its Applications, vol. 156, no. 2, pp. 262–267, 2008.
- F. Balibrea, J. Smítal, and M. Štefánková, “The three versions of distributional chaos,” Chaos, Solitons and Fractals, vol. 23, no. 5, pp. 1581–1583, 2005.
- T. Downarowicz, “Positive topological entropy implies chaos DC2,” In press.
- P. Oprocha, “Distributional chaos revisited,” Transactions of the American Mathematical Society, vol. 361, no. 9, pp. 4901–4925, 2009.
- P. Oprocha, “Weak mixing and product recurrence,” Annales de l'Institut Fourier, vol. 60, no. 4, pp. 1233–1257, 2010.
- G. Liao and Q. Fan, “Minimal subshifts which display Schweizer-Smítal chaos and have zero topological entropy,” Science in China A, vol. 41, no. 1, pp. 33–38, 1998.
- J. Dvořáková, “On a problem of iteration invariants for distributional chaos,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 2, pp. 785–787, 2012.