Continuous inverse shadowing and hyperbolicity
- 1 February 2003
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 67 (1), 15-26
- https://doi.org/10.1017/s0004972700033487
Abstract
We study the concepts of continuous shadowing and continuous inverse shadowing with respect to various classes of admissible pseudo orbits, and characterize hyperbolicity and structural stability using the notion of continuous inverse shadowing.Keywords
This publication has 11 references indexed in Scilit:
- Shadowing, expansiveness and hyperbolic homeomorphismsJournal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1996
- Diffeomorphisms with persistencyProceedings of the American Mathematical Society, 1996
- Hyperbolic homeomorphisms and bishadowingAnnales Polonici Mathematici, 1996
- Expansivity of semi-hyperbolic Lipschitz mappingsBulletin of the Australian Mathematical Society, 1995
- Approximate and Real Trajectories for Generic Dynamical SystemsJournal of Mathematical Analysis and Applications, 1995
- Diffeomorphisms in ℱ1(M) satisfy Axiom AErgodic Theory and Dynamical Systems, 1992
- The topological stability of diffeomorphismsNagoya Mathematical Journal, 1991
- Persistence in expansive systemsErgodic Theory and Dynamical Systems, 1983
- Topologically stable homeomorphisms of the circleNagoya Mathematical Journal, 1980
- Filtrations, Decompositions, and ExplosionsAmerican Journal of Mathematics, 1975