Saddles for expansive flows with the pseudo orbits tracing property
Jerzy Ombach
Annales Polonici Mathematici, Tome 55 (1991), p. 37-48 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

Let F be an expansive flow with the pseudo orbits tracing property on a compact metric space X. Suppose X is connected, locally connected and contains at least two distinct orbits. Then any point is a saddle.

Publié le : 1991-01-01
EUDML-ID : urn:eudml:doc:262268 
@article{bwmeta1.element.bwnjournal-article-apmv56z1p37bwm,
     author = {Jerzy Ombach},
     title = {Saddles for expansive flows with the pseudo orbits tracing property},
     journal = {Annales Polonici Mathematici},
     volume = {55},
     year = {1991},
     pages = {37-48},
     zbl = {0751.58032},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv56z1p37bwm}
}

Jerzy Ombach. Saddles for expansive flows with the pseudo orbits tracing property. Annales Polonici Mathematici, Tome 55 (1991) pp. 37-48. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv56z1p37bwm/

[000] [1] R. Bowen, Periodic orbits for hyperbolic flows, Amer. J. Math. 94 (1972), 1-37. | Zbl 0254.58005

[001] [2] R. Bowen and P. Walters, Expansive one-parameter flows, J. Differential Equations 12 (1972), 180-193. | Zbl 0242.54041

[002] [3] J. Franke and J. Selgrade, Hyperbolicity and chain recurrence, ibid. 26 (1977), 27-36. | Zbl 0329.58012

[003] [4] J. Ombach, Equivalent conditions for hyperbolic coordinates, Topology Appl. 23 (1986), 87-90. | Zbl 0597.58023

[004] [5] J. Ombach, Expansive homeomorphisms with the pseudo orbits tracing property, preprint 383, Institute of Math., Polish Acad. of Sci., 1987.

[005] [6] J. Ombach, Sinks, sources and saddles for expansive flows with the pseudo orbits tracing property, Ann. Polon. Math. 53 (1991), 237-252. | Zbl 0728.58025

[006] [7] W. Reddy, Expansive canonical coordinates are hyperbolic, Topology Appl. 15 (1983), 205-210. | Zbl 0502.54044

[007] [8] W. Reddy and L. Robertson, Sources, sinks and saddles for expansive homeomorphisms with canonical coordinates, Wesleyan University, preprint.

[008] [9] R. Thomas, Stability properties of one-parameter flows, Proc. London Math. Soc. 45 (1982), 479-505. | Zbl 0449.28019

[009] [10] R. Thomas, Topological stability: some fundamental properties, J. Differential Equations 59 (1985), 103-122. | Zbl 0545.34035

[010] [11] R. Thomas, Entropy of expansive flows, Ergodic Theory Dynamical Systems, 7 (1987), 611-625. | Zbl 0612.28015

[011] [12] R. Thomas, Canonical coordinates and the pseudo orbit tracing property, J. Differential Equations 90 (1991), 316-343. | Zbl 0737.58045

[012] [13] H. Whitney, Regular families of curves, Ann. of Math. 34 (1933), 244-270. | Zbl 0006.37101