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Primitive equations with horizontal viscosity: The initial value and The time-periodic problem for physical boundary conditions
Extensions of expansive dynamical systems
Departamento de Matemática y Estadística del Litoral, Centro Universitario Regional Litoral Norte, Universidad de la República, 25 de Agosto 281, Salto (50000), Uruguay |
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.
References:
| [1] |
M. Achigar, A note on Anosov homeomorphisms, Axioms, 8 (2019), 54.
doi: 10.3390/axioms8020054. |
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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. |
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J. P. Aubin and H. Frankowska, Set-valued Analysis, Systems & control, Birkhäuser, 1990. |
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B. F. Bryant,
Expansive self-homeomorphisms of a compact metric space, Amer. Math. Monthly, 69 (1962), 386-391.
doi: 10.1080/00029890.1962.11989902. |
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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. |
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J. L. Kelley, General Topology, D. Van Nostrand Co., 1955. |
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H. B. Keynes and J. B. Robertson,
Generators for topological entropy and expansiveness, Math. Systems Theory, 3 (1969), 51-59.
doi: 10.1007/BF01695625. |
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J. Lewowicz,
Persistence in expansive systems, Ergodic Theory Dynam. Systems, 3 (1983), 567-578.
doi: 10.1017/S0143385700002157. |
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S. Nadler, Continuum Theory: An Introduction, Chapman & Hall/CRC Pure and Applied Mathematics, Taylor & Francis, 1992.
doi: 10.1201/9781315274089. |
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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. |
show all references
References:
| [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. |
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