A -theoretic invariant for dynamical systems

Author:
Yiu Tung Poon

Journal:
Trans. Amer. Math. Soc. **311** (1989), 515-533

MSC:
Primary 46L80; Secondary 19K14, 28D20, 46L55

DOI:
https://doi.org/10.1090/S0002-9947-1989-0978367-5

MathSciNet review:
978367

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Abstract: Let be a zero-dimensional dynamical system. We consider the quotient group , where is the group of continuous integer-valued functions on and is the subgroup of functions of the form . We show that if is topologically transitive, then there is a natural order on which makes an ordered group. This order structure gives a new invariant for the classification of dynamical systems. We prove that for each , the number of fixed points of is an invariant of the ordered group . Then we show how can be computed as a direct limit of finite rank ordered groups. This is used to study the conditions under which is a dimension group. Finally we discuss the relation between and the -group of the crossed product -algebra associated to the system .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1989-0978367-5

Keywords:
Invariant for dynamical systems,
invariants for crossed products,
ordering in -groups,
direct limits

Article copyright:
© Copyright 1989
American Mathematical Society