INVERSE SHADOWING FOR EXPANSIVE FLOWS

Abstract

We extend the notion of inverse shadowing defined for diffeomorphisms to flows, and show that an expansive flow on a compact manifold with the shadowing property has the inverse shadowing property with respect to the classes of continuous methods. As a corollary we obtain that a hyperbolic flow also has the inverse shadowing property with respect to the classes of continuous methods.

Keywords

• flow;
• expansive;
• method;
• shadowing;
• inverse shadowing

File

Download PDF

References

1. J. Differential Equations v.12 Expansive one-parameter flows R.Bowen;P.Walters https://doi.org/10.1016/0022-0396(72)90013-7
2. J. Math. Anal. Appl. v.189 Approximate and real trajectories for generic dynamical systems R.Corless;S.Pilyugin https://doi.org/10.1006/jmaa.1995.1027
3. International J. of Bifurcation and Chaos v.12 Bishadowing and hyperbolicity P.Diamond;Y.Han;K.Lee https://doi.org/10.1142/S0218127402005455
4. Ann. Polon Math. v.65 Hyperbolic homeomorphisms and bishadowing P.Kloeden;J.Ombach https://doi.org/10.4064/ap-65-2-171-177
5. Functional Differential Equations v.6 Continuous and inverse shadowing P.Kloeden;J.Ombach;A.Pokrovskii
6. Bull. Austral. Math. Soc. v.67 Continuous inverse shadowing and hyperbolicity K.Lee https://doi.org/10.1017/S0004972700033487
7. Ann. Pol. Math. v.53.3 Sinks, sources and saddles for expansive flows with the pseudo orbit tracing property J.Ombach
8. J. Differential Equations v.140 Shadowing in structurally stable flows S.Pilyugin https://doi.org/10.1006/jdeq.1997.3295
9. Lecture Notes in Math. v.1706 Shadowing in dynamical systms S.Pilyugin
10. Discrete and Continuous Dynamical Systems v.8 Inverse shadowing by continuous methods S.Pilyugin https://doi.org/10.3934/dcds.2002.8.29
11. Proc. London Math. Soc. v.45 Stability properties of one-parameter flows R.Thomas https://doi.org/10.1112/plms/s3-45.3.479
12. J. Differential Equations v.90 Cannonical coordinates and the pseudo orbit tracing property R.Thomas https://doi.org/10.1016/0022-0396(91)90151-X

Cited by

1. Lipschitz inverse shadowing for non-singular flows vol.29, pp.1, 2014, https://doi.org/10.1080/14689367.2013.842958
2. Inverse shadowing for structurally stable flows vol.19, pp.4, 2004, https://doi.org/10.1080/1468936042000269569
3. Divergence-free vector fields with inverse shadowing vol.2013, pp.1, 2013, https://doi.org/10.1186/1687-1847-2013-337