# C*-algebras associated with reversible extensions of logistic maps

## Abstract

The construction of reversible extensions of dynamical systems presented in a previous paper by the author and A.V. Lebedev is enhanced, so that it applies to arbitrary mappings (not necessarily with open range). It is based on calculating the maximal ideal space of C*-algebras that extends endomorphisms to partial automorphisms via partial isometric representations, and involves a new set of 'parameters' (the role of parameters is played by chosen sets or ideals). As model examples, we give a thorough description of reversible extensions of logistic maps and a classification of systems associated with compression of unitaries generating homeomorphisms of the circle. Bibliography: 34 titles.

- Authors:

- Institute of Mathematics, University of Bialystok (Poland)

- Publication Date:

- OSTI Identifier:
- 22094052

- Resource Type:
- Journal Article

- Journal Name:
- Sbornik. Mathematics

- Additional Journal Information:
- Journal Volume: 203; Journal Issue: 10; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ALGEBRA; CLASSIFICATION; COMPRESSION; MAPPING; MATHEMATICAL SPACE

### Citation Formats

```
Kwasniewski, Bartosz K.
```*C*-algebras associated with reversible extensions of logistic maps*. United States: N. p., 2012.
Web. doi:10.1070/SM2012V203N10ABEH004271.

```
Kwasniewski, Bartosz K.
```*C*-algebras associated with reversible extensions of logistic maps*. United States. doi:10.1070/SM2012V203N10ABEH004271.

```
Kwasniewski, Bartosz K. Wed .
"C*-algebras associated with reversible extensions of logistic maps". United States. doi:10.1070/SM2012V203N10ABEH004271.
```

```
@article{osti_22094052,
```

title = {C*-algebras associated with reversible extensions of logistic maps},

author = {Kwasniewski, Bartosz K},

abstractNote = {The construction of reversible extensions of dynamical systems presented in a previous paper by the author and A.V. Lebedev is enhanced, so that it applies to arbitrary mappings (not necessarily with open range). It is based on calculating the maximal ideal space of C*-algebras that extends endomorphisms to partial automorphisms via partial isometric representations, and involves a new set of 'parameters' (the role of parameters is played by chosen sets or ideals). As model examples, we give a thorough description of reversible extensions of logistic maps and a classification of systems associated with compression of unitaries generating homeomorphisms of the circle. Bibliography: 34 titles.},

doi = {10.1070/SM2012V203N10ABEH004271},

journal = {Sbornik. Mathematics},

issn = {1064-5616},

number = 10,

volume = 203,

place = {United States},

year = {2012},

month = {10}

}

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