Hostname: page-component-848d4c4894-mwx4w Total loading time: 0 Render date: 2024-07-01T02:14:05.643Z Has data issue: false hasContentIssue false
  • English
  • Français

Parallelisability in Banach spaces: a parallelisable dynamical system with uniformly bounded trajectories

Published online by Cambridge University Press:  14 November 2011

B. M. Garay
B. M. Garay
Affiliation:
Department of Mathematics, University of Technology, H-1521 Budapest, Hungary
Get access Rights & Permissions [Opens in a new window]

Synopsis

In the Banach space of real sequences which converge to zero with the supremum norm, we construct a parallelisable dynamical system with uniformly-bounded trajectories.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 108 , Issue 3-4 , 1988 , pp. 371 - 378
Copyright
Copyright © Royal Society of Edinburgh 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Bhatia, N. P. and Szego, G. P.. Dynamical systems: stability theory and applications (Berlin: Springer, 1967).CrossRefGoogle Scholar
2Coban, M. M.. On the behaviour of metrizability under quotient s-mappings. Dokl. Akad. Nauk. UzSSR 166 (1966), 141–144.Google Scholar
3Engelking, R.. General topology (Warsaw: PWN, 1977).Google Scholar
4Garay, B. M.. Parallelizability in Banach spaces: applications of negligibility theory. Ada Math. Hungar. (to appear).Google Scholar
5Hajek, O.. Parallelizability revisited. Proc. Amer. Math. Soc. 27 (1971), 77–84.CrossRefGoogle Scholar
6Harrison, J. and Yorke, J. A.. Flows on S3 and R3 without periodic orbits. Geometric dynamics, ed. Palis, J. Jr, pp. 401–407 (Berlin: Springer, 1983).CrossRefGoogle Scholar
7Jones, G. S. and Yorke, J. A.. The existence and nonexistence of critical points in bounded flows. J. Differential Equations 6 (1969), 238–246.CrossRefGoogle Scholar
8Kuperberg, K. and Reed, C.. A rest-point free dynamical system on R 3 with uniformly bounded trajectories. Fund. Math. 114 (1981), 229–234.CrossRefGoogle Scholar
9Ponomarev, V.. Axioms of countability and continuous mappings. Bull. Acad. Polon 8 (1960), 127–134.Google Scholar
10Ulam, S. M.. The Scottish Book (Boston: Birkhauser, 1981).Google Scholar
11Vogt, E.. Review on a paper by K. Kuperberg and C. Reed. Fund. Math. 114 (1981), 229–234; Zbl. 508 (1983), 58036.Google Scholar
12Webb, G. F.. Compactness of bounded trajectories of dynamical systems in infinite-dimensional spaces. Proc. Rov. Soc. Edinburgh Sect. A 84 (1979), 19–33.CrossRefGoogle Scholar
13Wilson, W. F.. On the minimal sets of nonsingular vector fields. Ann. of Math. 84 (1966), 529–536.CrossRefGoogle Scholar