Hostname: page-component-7b7567c8c-kwt9d Total loading time: 0 Render date: 2026-11-12T21:03:33.634Z Has data issue: false hasContentIssue false
  • English
  • Français

Chaos and topological entropy in dimension n>1

Published online by Cambridge University Press:  19 September 2008

Covadonga Blanco García
Covadonga Blanco García
Affiliation:
Departamento de Ecuaciones Funcionales, Faculdad de Matemáticas, Universidad de Santiago de Compostela(La Coruña), Spain
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

In this paper we present a generalization to higher dimensions of the techniques for computation of the entropy of graphs in dimension one. Following these methods, we obtain a lower bound for the topological entropy of a differentiable map F:ℝn→ℝn possessing a snap-back repeller.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 2 , June 1986, pp. 163 - 165
Copyright
Copyright © Cambridge University Press 1986

References

REFERENCES

[1]Adler, R. L., Konheim, A. G. & McAndrew, M. H.. Topological entropy. Trans. Amer. Math. Soc. 114 (1965), 309–319.CrossRefGoogle Scholar
[2]Blanco, C. & Rodríguez, J. A.. Caos y entropía topológica para la ecuación diferencial con retardo. Actas VI C.E.D.Y.A. pp. 220–226Zaragoza (1983).Google Scholar
[3]Block, L., Guckenheimer, J., Misiurewicz, M. & Young, L.-S.. Periodic points and topological entropy of one dimensional maps. In Global Theory of Dynamical Systems, Proceedings, pp. 18–34. North-Western, 1979. Lecture Notes in Math. No 819. Springer: Berlin, 1980.CrossRefGoogle Scholar
[4]Heiden, U. & Walther, H.-O.. Existence of chaos in control systems with delayed feedback. J. Differential Equations. 47. No 2 (1983), 1–29.Google Scholar
[5]Li, T.-Y. & Yorke, J. A.. Period three implies chaos. Amer. Math. Monthly. 82 (1975), 985–992.CrossRefGoogle Scholar
[6]Mackey, M. & Glass, L.. Oscillations and chaos in physiological control systems. Science 197 (1977), 287–299.CrossRefGoogle ScholarPubMed
[7]Marotto, F. R.. Snap-back repellers imply chaos in ℝn. J. Math. Anal. & Appl. 63 (1978), 199–223.CrossRefGoogle Scholar
[8]Morris, H. C., Ryan, E. E. & Dodd, R. K.. Periodic solutions and chaos in a delay-differential equation modelling haematopoiesis. Nonlinear Anal. 7. No 6 (1983), 523–660.CrossRefGoogle Scholar