Topological stability for homeomorphisms with global attractor
Canadian mathematical bulletin, Tome 67 (2024) no. 2, pp. 493-503
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We prove that every topologically stable homeomorphism with global attractor of $\mathbb {R}^n$ is topologically stable on its global attractor. The converse is not true. On the other hand, if a homeomorphism with global attractor of a locally compact metric space is expansive and has the shadowing property, then it is topologically stable. This extends the Walters stability theorem (Walters, On the pseudo-orbit tracing property and its relationship to stability. The structure of attractors in dynamical systems, 1978, pp. 231–244).
Morales, Carlos Arnoldo; Nguyen, Nguyen Thanh. Topological stability for homeomorphisms with global attractor. Canadian mathematical bulletin, Tome 67 (2024) no. 2, pp. 493-503. doi: 10.4153/S0008439523000917
@article{10_4153_S0008439523000917,
author = {Morales, Carlos Arnoldo and Nguyen, Nguyen Thanh},
title = {Topological stability for homeomorphisms with global attractor},
journal = {Canadian mathematical bulletin},
pages = {493--503},
year = {2024},
volume = {67},
number = {2},
doi = {10.4153/S0008439523000917},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439523000917/}
}
TY - JOUR AU - Morales, Carlos Arnoldo AU - Nguyen, Nguyen Thanh TI - Topological stability for homeomorphisms with global attractor JO - Canadian mathematical bulletin PY - 2024 SP - 493 EP - 503 VL - 67 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008439523000917/ DO - 10.4153/S0008439523000917 ID - 10_4153_S0008439523000917 ER -
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