We characterize and describe the extensions of expansive and Ano- sov homeomorphisms on compact spaces. As an application we obtain a stability result for extensions of Anosov systems, and show a construction that embeds any expansive system inside an expansive system having the shadowing property for the pseudo orbits of the original space.
Citation: |
[1] |
M. Achigar, A note on Anosov homeomorphisms, Axioms, 8 (2019), 54.
doi: 10.3390/axioms8020054.![]() ![]() |
[2] |
M. Achigar, A. Artigue and I. Monteverde, Expansive homeomorphisms on non-Hausdorff spaces, Topol. Appl., 207 (2016), 109-122.
doi: 10.1016/j.topol.2016.04.016.![]() ![]() ![]() |
[3] |
J. P. Aubin and H. Frankowska, Set-valued Analysis, Systems & control, Birkhäuser, 1990.
![]() ![]() |
[4] |
B. F. Bryant, Expansive self-homeomorphisms of a compact metric space, Amer. Math. Monthly, 69 (1962), 386-391.
doi: 10.1080/00029890.1962.11989902.![]() ![]() ![]() |
[5] |
M. Cerminara and M. Sambarino, Stable and unstable sets of $C^0$ perturbations of expansive homeomorphisms of surfaces, Nonlinearity, 12 (1999), 321-332.
doi: 10.1088/0951-7715/12/2/011.![]() ![]() ![]() |
[6] |
J. L. Kelley, General Topology, D. Van Nostrand Co., 1955.
![]() ![]() |
[7] |
H. B. Keynes and J. B. Robertson, Generators for topological entropy and expansiveness, Math. Systems Theory, 3 (1969), 51-59.
doi: 10.1007/BF01695625.![]() ![]() ![]() |
[8] |
J. Lewowicz, Persistence in expansive systems, Ergodic Theory Dynam. Systems, 3 (1983), 567-578.
doi: 10.1017/S0143385700002157.![]() ![]() ![]() |
[9] |
S. Nadler, Continuum Theory: An Introduction, Chapman & Hall/CRC Pure and Applied Mathematics, Taylor & Francis, 1992.
doi: 10.1201/9781315274089.![]() ![]() |
[10] |
P. Walters, On the pseudo orbit tracing property and its relationship to stability, The Structure of Attractors in Dynamical Systems, Lecture Notes in Math., 668 (1978), 231-244.
doi: 10.1007/BFb0101795.![]() ![]() ![]() |