Saddles for expansive flows with the pseudo orbits tracing property

Jerzy Ombach

Annales Polonici Mathematici (1991)

  • Volume: 56, Issue: 1, page 37-48
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Jerzy Ombach. "Saddles for expansive flows with the pseudo orbits tracing property." Annales Polonici Mathematici 56.1 (1991): 37-48. <http://eudml.org/doc/262268>.

@article{JerzyOmbach1991,
abstract = {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.},
author = {Jerzy Ombach},
journal = {Annales Polonici Mathematici},
keywords = {expansive flow; pseudo-orbit tracing property; saddle point},
language = {eng},
number = {1},
pages = {37-48},
title = {Saddles for expansive flows with the pseudo orbits tracing property},
url = {http://eudml.org/doc/262268},
volume = {56},
year = {1991},
}

TY - JOUR
AU - Jerzy Ombach
TI - Saddles for expansive flows with the pseudo orbits tracing property
JO - Annales Polonici Mathematici
PY - 1991
VL - 56
IS - 1
SP - 37
EP - 48
AB - 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.
LA - eng
KW - expansive flow; pseudo-orbit tracing property; saddle point
UR - http://eudml.org/doc/262268
ER -

References

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  1. [1] R. Bowen, Periodic orbits for hyperbolic flows, Amer. J. Math. 94 (1972), 1-37. Zbl0254.58005
  2. [2] R. Bowen and P. Walters, Expansive one-parameter flows, J. Differential Equations 12 (1972), 180-193. Zbl0242.54041
  3. [3] J. Franke and J. Selgrade, Hyperbolicity and chain recurrence, ibid. 26 (1977), 27-36. Zbl0329.58012
  4. [4] J. Ombach, Equivalent conditions for hyperbolic coordinates, Topology Appl. 23 (1986), 87-90. Zbl0597.58023
  5. [5] J. Ombach, Expansive homeomorphisms with the pseudo orbits tracing property, preprint 383, Institute of Math., Polish Acad. of Sci., 1987. 
  6. [6] J. Ombach, Sinks, sources and saddles for expansive flows with the pseudo orbits tracing property, Ann. Polon. Math. 53 (1991), 237-252. Zbl0728.58025
  7. [7] W. Reddy, Expansive canonical coordinates are hyperbolic, Topology Appl. 15 (1983), 205-210. Zbl0502.54044
  8. [8] W. Reddy and L. Robertson, Sources, sinks and saddles for expansive homeomorphisms with canonical coordinates, Wesleyan University, preprint. 
  9. [9] R. Thomas, Stability properties of one-parameter flows, Proc. London Math. Soc. 45 (1982), 479-505. Zbl0449.28019
  10. [10] R. Thomas, Topological stability: some fundamental properties, J. Differential Equations 59 (1985), 103-122. Zbl0545.34035
  11. [11] R. Thomas, Entropy of expansive flows, Ergodic Theory Dynamical Systems, 7 (1987), 611-625. Zbl0612.28015
  12. [12] R. Thomas, Canonical coordinates and the pseudo orbit tracing property, J. Differential Equations 90 (1991), 316-343. Zbl0737.58045
  13. [13] H. Whitney, Regular families of curves, Ann. of Math. 34 (1933), 244-270. Zbl0006.37101

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