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We extend Jung's result about the relations among bi-closing, open and constant-to-one codes between general shift spaces to closing codes. We also show that any closing factor code $ \varphi:X\rightarrow Y $ has a degree $ d $, and it is proved that $ d $ is the minimal number of preimages of points in $ Y $. Some other properties of closing codes are provided. Then, we show that any closing factor code is hyperbolic. This enables us to determine some shift spaces which preserved by closing codes.
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참고문헌 (11)
참고문헌 신청
F. Blanchard / 1991 / Extensions a fibre constante / Ergod. Th. & Dynam. Sys. 11:7~17
M. Boyle / 1987 / Resolving maps and the dimension group for shifts of finite type / Mem. Amer. Math. Soc. 70(377)
M. Brin / 2002 / Introduction to Dynamical Systems / Cambridge University Press
D. Fiebig / 1995 / Common extensions and hyperbolic factor maps for coded systems / Ergod. Th. & Dynam. Sys. 15:517~534
D. Fiebig / 1991 / Covers for coded systems, in Symbolic dynamics and its applications;Contemp. Math., 135 :139~179
M. Boyle / 1987 / Resolving maps and the dimension group for shifts of finite type / Mem. Amer. Math. Soc. 70(377)
M. Brin / 2002 / Introduction to Dynamical Systems / Cambridge University Press
D. Fiebig / 1995 / Common extensions and hyperbolic factor maps for coded systems / Ergod. Th. & Dynam. Sys. 15:517~534
D. Fiebig / 1991 / Covers for coded systems, in Symbolic dynamics and its applications;Contemp. Math., 135 :139~179
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