Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-23T22:20:34.032Z Has data issue: false hasContentIssue false
  • English
  • Français

Invariant measures for the flow of a first order partial differential equation

Published online by Cambridge University Press:  19 September 2008

R. Rudnicki
R. Rudnicki
Affiliation:
Institute of Mathematics, Silesian University40-007 Katowice, Poland
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.

We prove that the dynamical systems generated by first order partial differential equations are K-flows and chaotic in the sense of Auslander & Yorke.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 3 , September 1985 , pp. 437 - 443
Copyright
Copyright © Cambridge University Press 1985

References

REFERENCES

[1]Auslander, J. & Yorke, J.. Interval maps, factors of maps and chaos. Tôhoku Math. J. II. Ser., 32 (1980), 177–188.Google Scholar
[2]Brunovsky, P.. Notes on chaos in the cell population partial differential equation. Nonlinear Analysis 7 (1983), 167–176.CrossRefGoogle Scholar
[3]Brunovský, P. & Komornik, J.. Ergodicity and exactness of the shift on C∞] and the semiflow of a first order partial differential equation. To appear.Google Scholar
[4]Dawidowicz, A. L.. On existence of invariant measure for the dynamical system generated by partial differential equation. Ann. Polon. Math. XXXIX (1983), 129–137.CrossRefGoogle Scholar
[5]Lasota, A.. Invariant measures and a linear model of turbulence. Rend. Sent. Mat. Univ. Padova 61 (1979), 40–48.Google Scholar
[6]Lasota, A.. Stable and chaotic solutions of a first order partial differential equation. Nonlinear Analysis 5 (1981), 1181–1193.CrossRefGoogle Scholar